biblio_local.bib

@ARTICLE{Zwamborn1992,
  title    = "The three dimensional weak form of the conjugate gradient {FFT}
              method for solving scattering problems",
  author   = "Zwamborn, P and van den Berg, P M",
  abstract = "The problem of electromagnetic scattering by a three-dimensional
              dielectric object can be formulated in terms of a hypersingular
              integral equation, in which a grad-div operator acts on a vector
              potential. The vector potential is a spatial convolution of the
              free space Green's function and the contrast source over the
              domain of interest. A weak form of the integral equation for the
              relevant unknown quantity is obtained by testing it with
              appropriate testing functions. The vector potential is then
              expanded in a sequence of the appropriate expansion functions and
              the grad-div operator is integrated analytically over the
              scattering object domain only. A weak form of the singular
              Green's function has been used by introducing its spherical mean.
              As a result, the spatial convolution can be carried out
              numerically using a trapezoidal integration rule. This method
              shows excellent numerical performance",
  journal  = "IEEE Trans. Microw. Theory Tech.",
  volume   =  40,
  number   =  9,
  pages    = "1757--1766",
  month    =  sep,
  year     =  1992,
  keywords = "Green's function methods;conjugate gradient
              methods;electromagnetic wave scattering;fast Fourier
              transforms;integral equations;3D object;conjugate gradient FFT
              method;electromagnetic scattering;expansion functions;free space
              Green's function;grad-div operator;hypersingular integral
              equation;spatial convolution;three dimensional weak
              form;three-dimensional dielectric object;trapezoidal integration
              rule;vector potential;Convolution;Dielectrics;Electromagnetic
              diffraction;Electromagnetic scattering;Fast Fourier
              transforms;Integral equations;Moment
              methods;Tellurium;Testing;Wave functions"
}

@ARTICLE{Zhang2004,
  title       = "Three-dimensional nonlinear image reconstruction for microwave
                 biomedical imaging",
  author      = "Zhang, Zhong Qing and Liu, Qing Huo",
  affiliation = "Department of Electrical and Computer Engineering, Duke
                 University, Durham, NC 27708-0291, USA.",
  abstract    = "Active microwave imaging has attracted significant interests
                 in biomedical applications, in particular for breast imaging.
                 However, the high electrical contrasts in breast tissue also
                 increases the difficulty of forming an accurate image because
                 of the increased multiple scattering. To model such strong
                 three-dimensional (3-D) multiple scattering effects in
                 biomedical imaging applications, we develop a full 3-D inverse
                 scattering algorithm based on the combination of the contrast
                 source inversion and the fast Fourier transform algorithm.
                 Numerical results show that our algorithm can accurately
                 invert for the high-contrast media in breast tissue.",
  journal     = "IEEE Trans. Biomed. Eng.",
  volume      =  51,
  number      =  3,
  pages       = "544--548",
  month       =  mar,
  year        =  2004
}

@ARTICLE{Zhang2003,
  title       = "Microwave breast imaging: {3-D} forward scattering simulation",
  author      = "Zhang, Zhong Qing and Liu, Qing Huo and Xiao, Chunjiang and
                 Ward, Erika and Ybarra, Gary and Joines, William T",
  affiliation = "Department of Electrical and Computer Engineering, Duke
                 University, Durham, NC 27708-0291, USA.",
  abstract    = "Active microwave imaging (MWI) is emerging as a promising
                 technique for the detection of biomedical anomalies such as
                 breast cancer because of the high electrical contrasts between
                 malignant tumors and normal tissue. Previously, we have
                 developed fast two-dimensional forward and inverse scattering
                 algorithms for MWI systems. In this paper, we report the full
                 three-dimensional (3-D) forward scattering simulation in order
                 to account for 3-D effects and to provide a fast solver in
                 future 3-D nonlinear inverse scattering methods. The 3-D fast
                 forward method is based on the stabilized biconjugate-gradient
                 fast Fourier transform (BCGS-FFT) algorithm. The method has
                 been validated for various MWI measurement scenarios. Using
                 this fast simulation method, we demonstrate the importance of
                 accounting for 3-D effects in MWI, and we compare numerical
                 results with the measurements from an experimental prototype.",
  journal     = "IEEE Trans. Biomed. Eng.",
  volume      =  50,
  number      =  10,
  pages       = "1180--1189",
  month       =  oct,
  year        =  2003
}

@ARTICLE{Zakaria2012,
  title    = "The {Finite-Element} Method Contrast Source Inversion Algorithm
              for {2D} Transverse Electric Vectorial Problems",
  author   = "Zakaria, A and LoVetri, J",
  abstract = "The contrast source inversion algorithm is formulated using the
              finite-element method for two-dimensional transverse electric
              microwave imaging problems. Edge-based triangular elements with
              vector basis functions are utilized to solve the TE
              electromagnetic problem. A single finite-element method (FEM)
              mesh is used to model both the electric field as well as the
              contrast-source and contrast variables used in the inverse
              problem. The electromagnetic field is modeled by taking the
              unknown values to be the tangential components of the transverse
              electric field along the edges of each triangular element. The
              unknown contrast-source and contrast variables are located at the
              centroids of every triangular element of the same FEM mesh, but
              only inside the imaging domain. The adaptation of the
              FEM-contrast source inversion (FEM-CSI) algorithm to 2D-TE
              problems on such an arbitrary mesh requires the implementation of
              special transformation operators which are presented herein. The
              algorithm's capabilities are demonstrated by inverting the
              Fresnel experimental TE datasets as well as synthetically
              generated data.",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  60,
  number   =  10,
  pages    = "4757--4765",
  month    =  oct,
  year     =  2012,
  keywords = "electric fields;electromagnetic fields;finite element
              analysis;microwave imaging;2D transverse electric vectorial
              problems;2D-TE problems;Fresnel experimental TE
              datasets;arbitrary mesh;contrast source inversion
              algorithm;contrast variables;edge-based triangular
              elements;electric field;electromagnetic field;finite-element
              method;single FEM mesh;synthetically generated data;tangential
              components;transformation operators;two-dimensional transverse
              electric microwave imaging problems;Finite element methods;Image
              edge detection;Image reconstruction;Imaging;Inverse
              problems;Transmitters;Vectors;Contrast source inversion
              (CSI);finite-element method (FEM);microwave
              imaging;transverse-electric"
}

@ARTICLE{Zakaria2011,
  title    = "Application of Multiplicative Regularization to the
              {Finite-Element} Contrast Source Inversion Method",
  author   = "Zakaria, A and LoVetri, J",
  abstract = "Multiplicative regularization is applied to the finite-element
              contrast source inversion (FEM-CSI) algorithm recently developed
              for microwave tomography. It is described for the two-dimensional
              (2D) transverse-magnetic (TM) case and tested by inverting
              experimental data where the fields can be approximated as TM. The
              unknown contrast, which is to be reconstructed, is represented
              using nodal variables and first-order basis functions on
              triangular elements; the same first-order basis functions used in
              the FEM solution of the accompanying field problem. This approach
              is different from other MR-CSI implementations where the contrast
              variables are located on a uniform grid of rectangular cells and
              represented using pulse basis functions. The linear basis
              function representation of the contrast makes it difficult to
              apply the weighted L2-norm total variation multiplicative
              regularization which requires that gradient and divergence
              operators be applied to the predicted contrast at each iteration
              of the inversion algorithm; the use of finite-difference
              operators for this purpose becomes unwieldy. Thus, a new
              technique is introduced to perform these operators on the
              triangular mesh.",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  59,
  number   =  9,
  pages    = "3495--3498",
  year     =  2011,
  keywords = "electromagnetic wave scattering;finite difference methods;finite
              element analysis;inverse problems;tomography;2D
              transverse-magnetic case;FEM-CSI algorithm;divergence
              operator;finite-difference operator;finite-element contrast
              source inversion method;first-order basis function;gradient
              operator;linear basis function;microwave
              tomography;multiplicative regularization;nodal variable;pulse
              basis function;triangular element;Antenna
              measurements;Electromagnetics;Finite element methods;Inverse
              problems;Microwave imaging;Microwave theory and
              techniques;Contrast source inversion;finite-element
              method;microwave tomography;multiplicative regularization"
}

@ARTICLE{Zakaria2010,
  title    = "Finite-element contrast source inversion method for microwave
              imaging",
  author   = "Zakaria, Amer and Gilmore, Colin and LoVetri, Joe",
  abstract = "With respect to the microwave imaging of the dielectric
              properties in an imaging region, the full derivation of a new
              inversion algorithm based on the contrast source inversion (CSI)
              algorithm and a finite-element method (FEM) discretization of the
              Helmholtz differential operator formulation for the scattered
              electromagnetic field is presented. The unknown dielectric
              properties are represented as nodal values on a two-dimensional
              (2D) arbitrary triangular mesh using linear basis functions. The
              use of FEM to represent the Helmholtz operator allows for the
              flexibility of having an inhomogeneous background medium, as well
              as the ability to accurately model any boundary shape or type:
              both conducting and absorbing. The resulting sparse and symmetric
              FEM matrix equation can be solved efficiently, and it is shown
              how its solution can be used to calculate the gradient operators
              required in the conjugate-gradient CSI update without storing the
              inverse of the FEM matrix. The inversion algorithm is applied to
              conductive-enclosures of various shapes and unbounded-region
              microwave tomography configurations where the 2D transverse
              magnetic (TM) approximation can be applied.",
  journal  = "Inverse Probl.",
  volume   =  26,
  number   =  11,
  pages    = "115010",
  year     =  2010
}

@ARTICLE{Zainud-Deen2008,
  title   = "Breast cancer detection using a hybrid Finite difference frequency
             domain and particle swarm optimization techniques",
  author  = "Zainud-Deen, S H and Hassen, Walaa M and Ali, E M and Awadalla, K
             H and Sharshar, H A",
  journal = "2008 National Radio Science Conference",
  year    =  2008
}

@ARTICLE{Yurkin2007,
  title   = "The discrete dipole approximation: An overview and recent
             developments",
  author  = "Yurkin, M A and Hoekstra, A G",
  journal = "J. Quant. Spectrosc. Radiat. Transf.",
  volume  =  106,
  number  = "1-3",
  year    =  2007
}

@ARTICLE{Yu2008,
  title    = "Active Microwave Imaging {II}: {3-D} System Prototype and Image
              Reconstruction From Experimental Data",
  author   = "Yu, Chun and Yuan, Mengqing and Stang, J and Bresslour, E and
              George, R T and Ybarra, G A and Joines, W T and Liu, Qing-Huo",
  abstract = "A 3-D microwave imaging system prototype and an inverse
              scattering algorithm are developed to demonstrate the feasibility
              of 3-D microwave imaging for medical applications such as breast
              cancer detection with measured data. In this experimental
              prototype, the transmitting and receiving antennas are placed in
              a rectangular tub containing a fluid. The microwave scattering
              data are acquired by mechanically scanning a single transmit
              antenna and a single receive antenna, thus avoiding the mutual
              coupling that occurs when an array is used. Careful design and
              construction of the system has yielded accurate measurements of
              scattered fields so that even the weak scattered signals at S21 =
              -90 dB (or 30 dB below the background fields) can be measured
              accurately. Measurements are performed in the frequency domain at
              several discrete frequencies. The collected 3-D experimental data
              in fluid are processed by a 3-D nonlinear inverse scattering
              algorithm to unravel the complicated multiple scattering effects
              and produce high-resolution 3-D digital images of the dielectric
              constant and conductivity of the imaging domain. Dielectric
              objects as small as 5 mm in size have been imaged effectively at
              1.74 GHz.",
  journal  = "IEEE Trans. Microw. Theory Tech.",
  volume   =  56,
  number   =  4,
  pages    = "991--1000",
  month    =  apr,
  year     =  2008,
  keywords = "antenna arrays;biomedical imaging;electromagnetic wave
              scattering;image reconstruction;image resolution;microwave
              imaging;3-D digital images;3-D microwave imaging system
              prototype;frequency 1.74 GHz;image reconstruction;medical
              applications;microwave scattering data;nonlinear inverse
              scattering algorithm;receiving antennas;size 5 mm;transmitting
              antennas;Born iterative method;breast cancer detection;diagonal
              tensor approximation;distorted Born iterative method;inverse
              scattering;microwave imaging;nonlinear inverse scattering
              algorithm;stabilized biconjugate-gradient fast Fourier transform
              (FFT) algorithm"
}

@ARTICLE{Xu2002,
  title   = "The Stabilized Biconjugate Gradient Fast Fourier 'Ikansform Method
             for Electromagnetic Scattering",
  author  = "Xu', Xuemin and Liu, Qing Huo and Zhang, Zhong Qing",
  journal = "IEEE",
  year    =  2002
}

@ARTICLE{Wiskin2012,
  title       = "Non-linear inverse scattering: high resolution quantitative
                 breast tissue tomography",
  author      = "Wiskin, J and Borup, D T and Johnson, S A and Berggren, M",
  affiliation = "Department Bioengineering, WEB, South Central Campus Dr, Rm
                 2750, Salt Lake City, Utah 84112, USA. j.w.wiskin@gmail.com",
  abstract    = "Recent published results in inverse scattering generally show
                 the difficulty in dealing with moderate to high contrast
                 inhomogeneities when employing linearized or iteratively
                 linearized algorithms (e.g., distorted Born iterative method).
                 This paper presents a fully nonlinear algorithm utilizing full
                 wave field data, that results in ultrasound computed
                 tomographic images from a laboratory breast scanner, and shows
                 several such unique images from volunteer subjects. The
                 forward problem, data collection process and inverse
                 scattering algorithm used are discussed. A functional that
                 represents the {"}best fit{"} between predicted and measured
                 data is minimized, and therefore requires a very fast forward
                 problem solver, Jacobian calculation, and gradient estimation,
                 all of which are described. The data collection device is
                 described. The algorithm and device yield quantitative
                 estimates of human breast tissue in vivo. Several high
                 resolution images, measuring ∼150 by 150 wavelengths, obtained
                 from the 2D inverse scattering algorithms, using data
                 collected from a first prototype, are shown and discussed. The
                 quantitative values are compared with previous published work.",
  journal     = "J. Acoust. Soc. Am.",
  volume      =  131,
  number      =  5,
  pages       = "3802--3813",
  month       =  may,
  year        =  2012,
  issn_alt    = "1520-8524"
}

@ARTICLE{Winters2010,
  title       = "A Sparsity Regularization Approach to the Electromagnetic
                 Inverse Scattering Problem",
  author      = "Winters, David W and Van Veen, Barry D and Hagness, Susan C",
  affiliation = "Department of Electrical and Computer Engineering, University
                 of Wisconsin, Madison, WI USA 53706.",
  abstract    = "We investigate solving the electromagnetic inverse scattering
                 problem using the distorted Born iterative method (DBIM) in
                 conjunction with a variable-selection approach known as the
                 elastic net. The elastic net applies both ℓ1 and ℓ2 penalties
                 to regularize the system of linear equations that result at
                 each iteration of the DBIM. The elastic net thus incorporates
                 both the stabilizing effect of the ℓ2 penalty with the
                 sparsity encouraging effect of the ℓ1 penalty. The DBIM with
                 the elastic net outperforms the commonly used ℓ2 regularizer
                 when the unknown distribution of dielectric properties is
                 sparse in a known set of basis functions. We consider two very
                 different 3-D examples to demonstrate the efficacy and
                 applicability of our approach. For both examples, we use a
                 scalar approximation in the inverse solution. In the first
                 example the actual distribution of dielectric properties is
                 exactly sparse in a set of 3-D wavelets. The performances of
                 the elastic net and ℓ2 approaches are compared to the ideal
                 case where it is known a priori which wavelets are involved in
                 the true solution. The second example comes from the area of
                 microwave imaging for breast cancer detection. For a given set
                 of 3-D Gaussian basis functions, we show that the elastic net
                 approach can produce a more accurate estimate of the
                 distribution of dielectric properties (in particular, the
                 effective conductivity) within an anatomically realistic 3-D
                 numerical breast phantom. In contrast, the DBIM with an ℓ2
                 penalty produces an estimate which suffers from multiple
                 artifacts.",
  journal     = "IEEE Trans. Antennas Propag.",
  volume      =  58,
  number      =  1,
  pages       = "145--154",
  month       =  "1~" # jan,
  year        =  2010
}

@ARTICLE{Van_den_Berg2009,
  title   = "Integral and finite-difference formulations of the contrast source
             inversion method",
  author  = "van den Berg, P M and Abubakar, A and Habashy, T M",
  journal = "2009 International Conference on Electromagnetics in Advanced
             Applications",
  year    =  2009
}

@ARTICLE{Van2008,
  title     = "An efficient {3D} integral equation method for computation of
               electromagnetic wavefields in a layered configuration containing
               inhomogeneous objects",
  author    = "Van, P M and Abubakar, A and Habashy, T M",
  abstract  = "Abstract-This paper is concerned with the source-type of
               integral equation to compute the electromagnetic scattering by
               an inhomogeneous 3D object in a planar layered medium in the
               frequency domain. By decomposing the scattered field into a
               particular and a general ...",
  journal   = "PIERS Proceedings",
  publisher = "piers.org",
  year      =  2008
}

@ARTICLE{Van_den_Berg2002,
  title    = "Inverse Scattering Algorithms Based on Contrast Source Integral
              Representations",
  author   = "van den Berg, Peter M and Abubakar, Aria",
  abstract = "This article reviews a number of algorithms to solve the
              nonlinear inverse scattering problem, where the discrepancy
              between the measured data and the predicted data is minimized.
              These algorithms are all based on a source type of integral
              representation of the scattered field, where the integral
              operator acts on a contrast source, being the product of the
              interior field and the contrast of the scattering object. Special
              attention is paid to the development of the
              contrast-source-inversion method, where the contrast sources are
              updated iteratively, and where, in each iteration, an explicit
              minimizer for the contrast is obtained. In particular, we discuss
              the effective implementation of a multiplicative constraint that
              minimizes the spatial variations of the contrast. We present
              actual reconstructions from both synthetic and experimental
              scattered field data.",
  journal  = "Inverse Probl. Sci. Eng.",
  volume   =  10,
  number   =  6,
  pages    = "559--576",
  year     =  2002
}

@ARTICLE{Van_den_Berg2001,
  title   = "Contrast Source Inversion Method: State of Art",
  author  = "van den Berg, P M and Abubakar, A",
  journal = "Prog. Electromagn. Res. B Pier B",
  volume  =  34,
  year    =  2001
}

@ARTICLE{Den_Berg1997,
  title    = "A contrast source inversion method",
  author   = "den Berg, Peter M van and Kleinman, Ralph E",
  abstract = "This paper describes a simple algorithm for reconstructing the
              complex index of refraction of a bounded object immersed in a
              known background from a knowledge of how the object scatters
              known incident radiation. The method described here is versatile
              accommodating both spatially and frequency varying incident
              fields and allowing a priori information about the scatterer to
              be introduced in a simple fashion. Numerical results show that
              this new algorithm outperforms the modified gradient approach
              which until now has been one of the most effective reconstruction
              algorithms available.",
  journal  = "Inverse Probl.",
  volume   =  13,
  number   =  6,
  pages    = "1607",
  year     =  1997
}

@ARTICLE{Den_Berg1995,
  title    = "A total variation enhanced modified gradient algorithm for
              profile reconstruction",
  author   = "den Berg, P M van and Kleinman, R E",
  abstract = "The total variation minimization method for deblurring noisy data
              is shown to be effective in dramatically increasing the
              resolution in a modified gradient approach to index of refraction
              reconstruction from measured scattered field data. Numerical
              evidence is presented which shows that by including the total
              variation in the functional to be minimized the reconstructions
              of piecewise constant profiles are considerably sharpened. The
              stability of the modified gradient method with respect to noise
              is apparently also enhanced. Furthermore, the presence of the
              total variation does not appear to adversely effect the
              established effectiveness of the modified gradient method in
              reconstructing smooth profiles.",
  journal  = "Inverse Probl.",
  volume   =  11,
  number   =  3,
  pages    = "L5",
  year     =  1995
}

@ARTICLE{Zakaria_nodate,
  title  = "The {Finite-Element} Contrast Source Inversion Method for Microwave
            Imaging Applications",
  author = "Zakaria, Amer"
}

@MISC{noauthor_undated-ua,
  title = "these\_Vautrin\_2011.pdf"
}

@ARTICLE{Automatique_undated-ac,
  title  = "Th\`{e}se de Doctorat de l'\'{E}cole Centrale de Nantes",
  author = "Automatique, Sp\'{e}cialit\'{e} : and Du Signal Et Informatique
            Appliqu\'{e}e, Traitement"
}

@MISC{noauthor_undated-to,
  title = "these\_Gilmore.pdf"
}

@ARTICLE{Doctorale_undated-cs,
  title  = "Ecole Centrale de Nantes",
  author = "Doctorale, \'{E}cole"
}

@MISC{noauthor_undated-dy,
  title = "these\_Alvaro.pdf"
}

@MISC{noauthor_undated-sm,
  title = "these\_Abubakar.pdf"
}

@ARTICLE{Semerci2012,
  title   = "A contrast source inversion method using truncated wavelet
             representations",
  author  = "Semerci, O and Li, M and Abubakar, A and Habashy, T M",
  journal = "Proceedings of the 2012 IEEE International Symposium on Antennas
             and Propagation",
  year    =  2012
}

@ARTICLE{Semenov2005,
  title    = "Microwave-tomographic imaging of the high dielectric-contrast
              objects using different image-reconstruction approaches",
  author   = "Semenov, S Y and Bulyshev, A E and Abubakar, A and Posukh, V G
              and Sizov, Y E and Souvorov, A E and van den Berg, P M and
              Williams, T C",
  abstract = "Microwave tomography is an imaging modality based on
              differentiation of dielectric properties of an object. The
              dielectric properties of biological tissues and its functional
              changes have high medical significance. Biomedical applications
              of microwave tomography are a very complicated and challenging
              problem, from both technical and image reconstruction
              point-of-views. The high contrast in tissue dielectric properties
              presenting significant advantage for diagnostic purposes
              possesses a very challenging problem from an image-reconstruction
              prospective. Different imaging approaches have been developed to
              attack the problem, such as two-dimensional (2-D) and
              three-dimensional (3-D), minimization, and iteration schemes. The
              goal of this research is to study imaging performance of the
              Newton and the multiplicative regularized contrast source
              inversion (MR-CSI) methods in 2-D geometry and gradient and
              MR-CSI methods in 3-D geometry using high-contrast, medium-size
              phantoms, and biological objects. Experiments were conducted on
              phantoms and excised segment of a pig hind-leg using a 3-D
              microwave-tomographic system operating at frequencies of 0.9 and
              2.05 GHz. Both objects being of medium size (10-15 cm) possess
              high dielectric contrasts. Reconstructed images were obtained
              using all imaging approaches. Different approaches are evaluated
              and discussed based on its performance and quality of
              reconstructed images.",
  journal  = "IEEE Trans. Microw. Theory Tech.",
  volume   =  53,
  number   =  7,
  pages    = "2284--2294",
  month    =  jul,
  year     =  2005,
  keywords = "Newton method;biological tissues;dielectric properties;gradient
              methods;image reconstruction;medical image processing;microwave
              imaging;phantoms;tomography;0.9 GHz;2.05 GHz;2D geometry;3D
              geometry;3D microwave tomographic system;MR-CSI method;Newton
              method;gradient methods;high dielectric-contrast objects;image
              reconstruction;microwave tomographic imaging;microwave
              tomography;multiplicative regularized contrast source
              inversion;Biological tissues;Biomedical
              imaging;Dielectrics;Geometry;Image reconstruction;Imaging
              phantoms;Medical diagnostic imaging;Microwave
              imaging;Tomography;Two dimensional displays;Dielectric
              properties;high contrast;microwave imaging;tomography"
}

@ARTICLE{Semenov2002,
  title       = "Three-dimensional microwave tomography: initial experimental
                 imaging of animals",
  author      = "Semenov, Serguei Y and Svenson, Robert H and Bulyshev,
                 Alexander E and Souvorov, Alexander E and Nazarov, Alexei G
                 and Sizov, Yuri E and Posukh, Vitaly G and Pavlovsky, Andrey
                 and Repin, Pavel N and Starostin, Andrey N and Voinov, Boris A
                 and Taran, Michael and Tatsis, George P and Baranov, Vladimir
                 Y",
  affiliation = "Carolinas Medical Center, Charlotte, NC 28203, USA.
                 ssemenov@carolinas.org",
  abstract    = "The purpose of this study was to construct a microwave
                 tomographic system capable of conducting experiments with
                 whole scale biological objects and to demonstrate the
                 feasibility of microwave tomography for imaging such objects
                 using a canine model. Experiments were conducted using a
                 three-dimensional (3-D) microwave tomographic system with
                 working chamber dimensions of 120 cm in diameter and 135 cm in
                 height. The operating frequency was 0.9 GHz. The object under
                 study was located in the central area of the tomographic
                 chamber filled with a salt solution. Experimentally measured
                 attenuation of the electromagnetic field through the thorax
                 was about -120 dB. To obtain images, we used various
                 two-dimensional and 3-D reconstruction schemes. Images of the
                 canine were obtained. In spite of imperfections, the images
                 represent a significant milestone in the development of
                 microwave tomography for whole body imaging and demonstrate
                 its feasibility.",
  journal     = "IEEE Trans. Biomed. Eng.",
  volume      =  49,
  number      =  1,
  pages       = "55--63",
  month       =  jan,
  year        =  2002
}

@ARTICLE{Scapaticci2012,
  title   = "A {FEASIBILITY} {STUDY} {ON} {MICROWAVE} {IMAGING} {FOR} {BRAIN}
             {STROKE} {MONITORING}",
  author  = "Scapaticci, Rosa and Di Donato, Loreto and Catapano, Ilaria and
             Crocco, Lorenzo",
  journal = "Prog. Electromagn. Res. B Pier B",
  volume  =  40,
  year    =  2012
}

@ARTICLE{Scapaticci2012,
  title    = "{Wavelet-Based} Adaptive Multiresolution Inversion for
              Quantitative Microwave Imaging of Breast Tissues",
  author   = "Scapaticci, R and Catapano, I and Crocco, L",
  abstract = "Microwave imaging is a feasible tool for medical imaging owing to
              the different electric properties of tissues. To this end, it is
              important to devise inversion procedures capable of achieving a
              reliable quantitative estimate of the tissues under test. With
              respect to breast screening, we propose a full-wave inversion
              method, which takes advantage of the adaptive multiresolution
              features of the wavelet basis to accommodate the trade off
              between spatial resolution and inversion stability. As shown
              through a preliminary numerical assessment on 2D anthropomorphic
              breast phantoms, the proposed approach is capable of achieving
              satisfying results without any a priori knowledge of breast
              shape, as well as of thickness and electric properties of the
              skin layer.",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  60,
  number   =  8,
  pages    = "3717--3726",
  month    =  aug,
  year     =  2012,
  keywords = "biological organs;biological tissues;medical image
              processing;microwave imaging;wavelet transforms;2D
              anthropomorphic breast phantoms;adaptive multiresolution
              features;breast screening;breast tissues;full-wave inversion
              method;inversion stability;medical imaging;numerical
              assessment;quantitative microwave imaging;skin layer;spatial
              resolution;wavelet basis;wavelet-based adaptive multiresolution
              inversion;Breast tissue;Discrete wavelet
              transforms;Imaging;Inverse problems;Permittivity;Breast
              cancer;electromagnetic scattering;inverse problems;microwave
              imaging;wavelet transform"
}

@MISC{noauthor_undated-nh,
  title = "Sarkar1986.pdf"
}

@ARTICLE{Rubaek2011,
  title    = "A Contrast Source Inversion Algorithm Formulated Using the
              {Log-Phase} Formulation",
  author   = "Rub\ae{}k, Tonny and Meaney, Paul M and Paulsen, Keith D",
  journal  = "Int. J. Antennas Propag.",
  volume   =  2011,
  pages    = "1--10",
  year     =  2011,
  issn_alt = "1687-5877"
}

@ARTICLE{Rubaek2009,
  title    = "Computational Validation of a {3-D} Microwave Imaging System for
              {Breast-Cancer} Screening",
  author   = "Rubaek, T and Kim, O S and Meincke, P",
  abstract = "The microwave imaging system currently being developed at the
              Technical University of Denmark is described and its performance
              tested on simulated data. The system uses an iterative
              Newton-based imaging algorithm for reconstructing the images in
              conjunction with an efficient method-of-moments solution of the
              associated forward scattering problem. A cylindrical multistatic
              antenna setup with 32 horizontally oriented antennas is used for
              collecting the data. It has been found that formulating the
              imaging algorithm in terms of the logarithm of the amplitude and
              the unwrapped phase of the measured signals improves its
              performance when compared to the more commonly used complex
              phasor formulation. This improvement is illustrated by imaging a
              simulated hemispherical breast model using both formulations. In
              addition to this, the importance of using the correct position
              and orientation of the antennas in the measurement system is
              shown by imaging the same breast model using a measurement setup
              in which the antennas are vertically oriented.",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  57,
  number   =  7,
  pages    = "2105--2115",
  month    =  jul,
  year     =  2009,
  keywords = "cancer;image reconstruction;iterative methods;mammography;medical
              image processing;method of moments;microwave
              imaging;physiological models;3-D microwave imaging;breast
              cancer;forward scattering problem;hemispherical breast
              model;image reconstruction;iterative Newton-based imaging
              algorithm;method-of-moments;multistatic antenna;phase
              unwrapping;Antenna measurements;Breast cancer;Computational
              modeling;Image reconstruction;Iterative algorithms;Iterative
              methods;Microwave imaging;Moment methods;Position
              measurement;System testing;Biomedical
              imaging;cancer;electromagnetic scattering inverse
              problems;microwave imaging;nonlinear equations"
}

@MISC{noauthor_undated-lf,
  title = "Roger1981.pdf"
}

@ARTICLE{Richmond1965,
  title   = "Scattering by a dielectric cylinder of arbitrary cross section
             shape",
  author  = "Richmond, J",
  journal = "IEEE Trans. Antennas Propag.",
  volume  =  13,
  number  =  3,
  year    =  1965
}

@ARTICLE{Remis_andPMvanden_undated-ec,
  title  = "On the equivalence of the {Newton-Kantorovich} and distorted Born
            methods",
  author = "Remis andPMvanden, R"
}

@ARTICLE{Rekanos2004,
  title    = "An inverse scattering approach based on the differential
              E-formulation",
  author   = "Rekanos, I T and Yioultsis, T V and Hilas, C S",
  abstract = "An inverse scattering technique based on the differential
              E-formulation in the frequency domain is proposed. The inversion
              is achieved by minimizing a cost functional, taking into account
              the discrepancy between measured and estimated field values,
              while the Helmholtz wave equation is set as constraint. The
              Fre\´chet derivatives of the cost functional with respect
              to the scatterer properties are derived analytically by means of
              the calculus of variations. Edge elements are used for the
              numerical treatment of the problem.",
  journal  = "IEEE Trans. Geosci. Remote Sens.",
  volume   =  42,
  number   =  7,
  pages    = "1456--1461",
  month    =  jul,
  year     =  2004,
  keywords = "differential equations;electromagnetic wave
              polarisation;electromagnetic wave scattering;geophysical
              techniques;microwave imaging;remote sensing;Frechet
              derivatives;Helmholtz wave equation;differential
              E-formulation;frequency domain;inverse scattering;microwave
              imaging;transverse electric polarization;Cost
              function;Geophysical measurements;Image reconstruction;Integral
              equations;Inverse problems;Iterative algorithms;Microwave
              imaging;Partial differential
              equations;Permittivity;Scattering;Differential
              formulation;Fr\échet derivatives;TE;inverse
              scattering;microwave imaging;polarization;transverse-electric"
}

@MISC{noauthor_undated-bd,
  title = "Rekanos1999.pdf"
}


@ARTICLE{Pastorino2007,
  title    = "Stochastic Optimization Methods Applied to Microwave Imaging: A
              Review",
  author   = "Pastorino, M",
  abstract = "Stochastic methods are now very common in electromagnetics. Among
              the various applications, they have been recently proposed for
              solving inverse problems arising in radio-frequency and microwave
              imaging. Some of the recently proposed stochastic inversion
              procedures are critically discussed (e.g., genetic algorithms,
              differential evolution methods, memetic algorithms, particle
              swarm optimizations, hybrid techniques, etc.) and the way they
              have been applied in this area. The use of the ant colony
              optimization method, which is a relatively new method in
              electromagnetics, is also proposed. Various imaging modalities
              are considered (tomography, buried object detection, and borehole
              sensing). Finally, the main features making these approaches
              useful for imaging purposes are discussed and the currently
              considered strategies to reduce the computational load associated
              with stochastic optimization procedures delineated",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  55,
  number   =  3,
  pages    = "538--548",
  month    =  mar,
  year     =  2007,
  keywords = "electromagnetic wave scattering;inverse problems;microwave
              imaging;optimisation;stochastic processes;ant colony optimization
              method;inverse problem;microwave imaging;stochastic optimization
              method;wave scattering;Buried object
              detection;Electromagnetics;Genetic algorithms;Inverse
              problems;Microwave imaging;Microwave theory and
              techniques;Optimization methods;Particle swarm optimization;Radio
              frequency;Stochastic processes;Ant colony optimization;genetic
              and evolutionary algorithms;genetic stochastic optimization
              methods;inverse scattering;microwave imaging"
}

@ARTICLE{Ozdemir2014,
  title    = "Cauchy Data Contrast Source Inversion Method",
  author   = "Ozdemir, O",
  abstract = "This letter introduces a computationally efficient inversion
              algorithm based on the contrast source inversion method for
              two-layered media applications. The proposed algorithm employs
              Cauchy data to derive an integral representation of the
              electromagnetic field inside the homogeneous neighborhood of the
              target. This representation yields a Lippmann-Schwinger-type
              integral equation that does not involve the background Green's
              function. Therefore, it provides a significant improvement in
              computational efficiency. Numerical experiments are provided to
              demonstrate the performance of the method.",
  journal  = "Geoscience and Remote Sensing Letters, IEEE",
  volume   =  11,
  number   =  4,
  pages    = "858--862",
  month    =  apr,
  year     =  2014,
  keywords = "image processing;inhomogeneous media;integral equations;Cauchy
              data contrast source inversion method;Lippmann-Schwinger type
              integral equation;computationally efficient inversion
              algorithm;electromagnetic field;homogeneous
              neighborhood;two-layered media application;Equations;Green's
              function methods;Imaging;Inverse
              problems;Media;Permittivity;Scattering;Contrast source inversion
              (CSI) method;inverse problems;microwave imaging"
}

@MISC{noauthor_undated-xr,
  title = "Omrane\_memoire\_05-07.pdf"
}

@ARTICLE{Oliveri2012,
  title   = "Inversion of {EM} scattering data through a multiresolution
             regularization approach within the contrast source formulation",
  author  = "Oliveri, Giacomo and Tommasi, Andrea and Massa, Andrea and
             Randazzo, Andrea and Pastorino, Matteo",
  journal = "Proceedings of the 2012 IEEE International Symposium on Antennas
             and Propagation",
  year    =  2012
}

@ARTICLE{Johnson_undated,
  title  = "Notes on Perfectly Matched Layers ({PMLs})",
  author = "Johnson, Steven G"
}

@ARTICLE{Optimization_undated-cr,
  title  = "Jorge Nocedal Stephen J. Wright",
  author = "Optimization, Numerical"
}

@ARTICLE{Mudry2012,
  title    = "Electromagnetic wave imaging of three-dimensional targets using a
              hybrid iterative inversion method",
  author   = "Mudry, Emeric and Chaumet, Patrick C and Belkebir, Kamal and
              Sentenac, Anne",
  abstract = "In microwave or optical wave imaging set-ups, the measured
              scattered field is usually not linearly linked to the target
              parameter of interest. To reconstruct the latter, nonlinearized
              or linearized iterative inversion techniques, such as the
              contrast source inversion method (CSI) or the conjugate gradient
              method (CGM) have been proposed (Litman and Crocco 2009 Inverse
              Problems 25 020201-5). In this paper, we adapt to the
              three-dimensional vectorial case, a hybrid method (HM) that
              combines the advantages of the CSI and CGM, and compare the
              performances of the different approaches using microwave
              experimental data. The HM appears to be the best compromise in
              terms of reconstruction accuracy, computation time and robustness
              to noise.",
  journal  = "Inverse Probl.",
  volume   =  28,
  number   =  6,
  pages    = "065007",
  year     =  2012
}

@ARTICLE{Mojabi2010,
  title    = "Eigenfunction contrast source inversion for circular metallic
              enclosures",
  author   = "Mojabi, Puyan and LoVetri, Joe",
  abstract = "The microwave imaging problem is considered where an object of
              interest is surrounded by a circular metallic enclosure. A new
              contrast source inversion (CSI) algorithm which uses
              eigenfunction expansions of the unknowns is presented for the
              reconstruction of the complex dielectric profile. Orthonormal
              eigenfunction expansions associated with the Helmholtz operator
              for a homogeneous medium and Dirichlet boundary conditions are
              used for the unknown contrast source and the contrast functions
              in the CSI functional. These are also used to express the
              incident field, which is assumed known, as well as for expanding
              the inverse Helmholtz operator in the CSI functional. The imaging
              domain is taken to be the whole interior of the metallic
              enclosure. No prior information, other than keeping the
              permittivity profile physical, is used. Results are provided for
              synthetic as well as experimental data. Based on the number of
              eigenfunctions used, a theoretical limit to the reconstruction
              quality is defined. Normalized errors relative to this
              theoretical limit are provided for each of the synthetic data
              sets.",
  journal  = "Inverse Probl.",
  volume   =  26,
  number   =  2,
  pages    = "025010",
  year     =  2010
}

@ARTICLE{Mojabi2009,
  title    = "Microwave Biomedical Imaging Using the Multiplicative Regularized
              {Gauss--Newton} Inversion",
  author   = "Mojabi, P and LoVetri, J",
  abstract = "The weighted L2-norm total variation multiplicative regularized
              Gauss-Newton inversion method, recently developed for inversion
              of low-frequency deep electromagnetic geophysical measurements,
              is used for microwave biomedical imaging. This inversion
              algorithm automatically adjusts the regularization weight and
              provides edge-preserving characteristics. The accuracy of this
              method is demonstrated by inverting experimental data of a human
              forearm and synthetic data taken from brain and breast models,
              both assuming two-dimensional (2D) transverse magnetic
              illumination.",
  journal  = "IEEE Antennas Wirel. Propag. Lett.",
  volume   =  8,
  pages    = "645--648",
  year     =  2009,
  keywords = "Newton method;medical image processing;microwave
              imaging;electromagnetic geophysical measurement;microwave
              biomedical imaging;multiplicative regularized Gauss-Newton
              inversion;regularization weight;Biomedical
              imaging;Gauss\–Newton method;inverse problems;microwave
              imaging (MWI);regularization"
}

@ARTICLE{Meaney2012,
  title   = "Ultrafast {3D} microwave tomography utilizing the direct dipole
             approximation",
  author  = "Meaney, P M and Grzegorczyk, T and Attardo, E and Paulsen, K D",
  journal = "2012 International Conference on Electromagnetics in Advanced
             Applications",
  year    =  2012
}

@ARTICLE{Meaney2007,
  title       = "Log transformation benefits parameter estimation in microwave
                 tomographic imaging",
  author      = "Meaney, Paul M and Fang, Qianqian and Rubaek, Tonny and
                 Demidenko, Eugene and Paulsen, Keith D",
  affiliation = "Thayer School of Engineering, Dartmouth College, Hanover New
                 Hampshire 03755, USA.",
  abstract    = "Microwave tomographic imaging falls under a broad category of
                 nonlinear parameter estimation methods when a Gauss-Newton
                 iterative reconstruction technique is used. A fundamental
                 requirement in using these approaches is evaluating the
                 appropriateness of the regression model. While there have been
                 numerous investigations of regularization techniques to
                 improve overall image quality, few, if any, studies have
                 explored the underlying statistical properties of the model
                 itself. The ordinary least squares (OLS) approach is used most
                 often, but there are other options such as the weighted least
                 squares (WLS), maximum likelihood (ML), and maximum a
                 posteriori (MAP) that may be more appropriate. In addition, a
                 number of variance stabilizing transformations can be applied
                 to make the inversion intrinsically more linear. In this
                 paper, a statistical analysis is performed of the properties
                 of the residual errors from the reconstructed images utilizing
                 actual measured data and it is demonstrated that the OLS
                 algorithm with a log transformation (OLSlog) is clearly
                 advantageous relative to the more commonly used OLS approach
                 by itself. In addition, several high contrast imaging
                 experiments are performed, which demonstrate that different
                 subsets of data are emphasized in each method and may
                 contribute to the overall image quality differences.",
  journal     = "Med. Phys.",
  volume      =  34,
  number      =  6,
  pages       = "2014--2023",
  month       =  jun,
  year        =  2007
}

@ARTICLE{Meaney2002a,
  title   = "{3D} scalar microwave image reconstruction algorithm",
  author  = "Meaney, P M and Fang, Qianqian and Geimer, S D and Streltsov, A V
             and Paulsen, K D",
  journal = "IEEE MTTS Int. Microw. Symp.",
  year    =  2002
}

@ARTICLE{Meaney2002b,
  title   = "Quantification of {3-D} field effects during {2-D} microwave
             imaging",
  author  = "Meaney, P M and Paulsen, K D and Geimer, S D and Haider, S A and
             Fanning, M W",
  journal = "IEEE Transactions on Biomedical Engineering",
  volume  =  49,
  number  =  7,
  year    =  2002
}

@article{Maniatis2000,
  title={Two-dimensional dielectric profile reconstruction based on spectral-domain moment method and nonlinear optimization},
  author={Maniatis, Theofanis A and Nikita, Konstantina S and Uzunoglu, Nikolaos K},
  journal={Microwave Theory and Techniques, IEEE Transactions on},
  volume={48},
  number={11},
  pages={1831--1840},
  year={2000},
  publisher={IEEE}
}

@ARTICLE{Lui2012,
  title       = "On the forward scattering of microwave breast imaging",
  author      = "Lui, Hoi-Shun and Fhager, Andreas and Persson, Mikael",
  affiliation = "Biomedical Electromagnetics Research Group, Division of Signal
                 Processing and Biomedical Engineering, Department of Signals
                 and Systems, Chalmers University of Technology, S 412 96
                 Gothenburg, Sweden.",
  abstract    = "Microwave imaging for breast cancer detection has been of
                 significant interest for the last two decades. Recent studies
                 focus on solving the imaging problem using an inverse
                 scattering approach. Efforts have mainly been focused on the
                 development of the inverse scattering algorithms, experimental
                 setup, antenna design and clinical trials. However, the
                 success of microwave breast imaging also heavily relies on the
                 quality of the forward data such that the tumor inside the
                 breast volume is well illuminated. In this work, a numerical
                 study of the forward scattering data is conducted. The
                 scattering behavior of simple breast models under different
                 polarization states and aspect angles of illumination are
                 considered. Numerical results have demonstrated that better
                 data contrast could be obtained when the breast volume is
                 illuminated using cross-polarized components in linear
                 polarization basis or the copolarized components in the
                 circular polarization basis.",
  journal     = "Int. J. Biomed. Imaging",
  volume      =  2012,
  pages       = "582037",
  month       =  "6~" # may,
  year        =  2012,
  issn_alt    = "1687-4196"
}

@ARTICLE{Li2013,
  title    = "A contrast source inversion method in the wavelet domain",
  author   = "Li, Maokun and Semerci, O\u{g}uz and Abubakar, Aria",
  abstract = "We present a contrast source inversion (CSI) algorithm using
              truncated wavelet representations. Specifically, we represent the
              unknown contrast sources and the contrast function in terms of
              the wavelet basis functions. In order to reduce the number of
              wavelet coefficients for these unknowns, we apply a progressive
              multiscale truncation scheme based on the reconstructed contrast
              function. This approach increases the robustness of the CSI
              algorithm for noisy or limited data, and decreases the
              computation time as well as the memory usage. We tested the
              wavelet-domain CSI method using both synthetic and experimental
              data. The numerical experiments show that similar results with
              the regular spatial-domain CSI method are obtained when the
              number of (independent) measurement data points is comparable to
              the number of the unknowns in the contrast function. The
              advantages of the wavelet-domain CSI method become apparent as we
              deal with cases where the number of measurement data points is
              smaller than the number of unknowns in the contrast function.",
  journal  = "Inverse Probl.",
  volume   =  29,
  number   =  2,
  pages    = "025015",
  year     =  2013
}

@ARTICLE{Li2012,
  title    = "A {Three-Dimensional} {Model-Based} Inversion Algorithm Using
              Radial Basis Functions for Microwave Data",
  author   = "Li, Maokun and Abubakar, A and Habashy, T M",
  abstract = "We present a three-dimensional (3D) model-based inversion
              algorithm for inverting electromagnetic data. In our approach,
              the models are described by points in the 3D space and the
              so-called radial basis functions are used as the interpolation
              functions for connecting these points. The use of the radial
              basis functions renders the surface of the target intrinsically
              smooth. The L2-norm and weighted L2-norm regularization schemes
              are employed to constrain the curvature and to further smooth the
              surface of the target. We tested this inversion algorithm using
              both synthetic and experimental data sets. The inversion results
              demonstrate that both the shapes and material properties of the
              target are well reconstructed. As a complementary algorithm to
              the pixel-based (tomographic) inversion algorithms, the
              model-based inversion algorithm has fewer parameters to invert;
              hence, it has a higher computational efficiency. The model-based
              inversion algorithm also gives the users the freedom to construct
              an initial model based on their knowledge and other related
              information. It helps to reduce the non-uniqueness in the data
              interpretation.",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  60,
  number   =  7,
  pages    = "3361--3372",
  month    =  jul,
  year     =  2012,
  keywords = "computational electromagnetics;interpolation;radial basis
              function networks;data interpretation;electromagnetic
              data;interpolation functions;microwave data;pixel-based inversion
              algorithms;radial basis functions;three-dimensional model-based
              inversion algorithm;tomographic inversion algorithms;weighted
              L2-norm regularization scheme;Computational
              modeling;Conductivity;Jacobian matrices;Level
              set;Manganese;Surface reconstruction;Three dimensional
              displays;Level set method;model-based inversion;nonlinear
              inversion;radial basis function;regularization"
}

@ARTICLE{Li1996,
author={Li, M. and Zhang, Q.-J. and Nakhla, M.},
journal={Microwaves, Antennas and Propagation, IEE Proceedings},
title={Finite difference solution of EM fields by asymptotic waveform techniques},
year={1996},
month={Dec},
volume={143},
number={6},
pages={512-520},
keywords={Helmholtz equations;Maxwell equations;dielectric properties;electromagnetic fields;finite difference methods;frequency-domain analysis;linear differential equations;waveguide theory;EM fields;FDTD;Helmholtz equations;Maxwell's equations;asymptotic waveform techniques;circuit simulation;complex-frequency hopping;dielectric cylinders;electromagnetic field problems;expanded asymptotic waveform evaluation;finite difference frequency domain;finite difference solution;finite difference technique;finite difference time domain;frequency-domain analysis;linear distributed circuits;linear lumped circuits;linear ordinary differential equations;spatial finite difference;speed up;stable technique;waveguides},
doi={10.1049/ip-map:19960749},
ISSN={1350-2417}
}

@article{Kleinman1992,
  title={A modified gradient method for two-dimensional problems in tomography},
  author={Kleinman, RE and Van den Berg, PM},
  journal={Journal of Computational and Applied Mathematics},
  volume={42},
  number={1},
  pages={17--35},
  year={1992},
  publisher={Elsevier}
}


@article{Kahnert2003,
  title={Numerical methods in electromagnetic scattering theory},
  author={Kahnert, F Michael},
  journal={Journal of Quantitative Spectroscopy and Radiative Transfer},
  volume={79},
  pages={775--824},
  year={2003},
  publisher={Elsevier}
}


@ARTICLE{Joachimowicz1991,
  title    = "Inverse scattering: an iterative numerical method for
              electromagnetic imaging",
  author   = "Joachimowicz, N and Pichot, C and Hugonin, J-P",
  abstract = "The authors propose a spatial iterative algorithm for
              electromagnetic imaging based on a Newton-Kantorovich procedure
              for the reconstruction of the complex permittivity of
              inhomogeneous lossy dielectric objects with arbitrary shape.
              Starting from integral representation of the electric field and
              using the moment method, this technique has been developed for
              2-D (for TM and TE polarization cases) objects as well as for 3-D
              objects. Its performance has been compared with spectral
              techniques of classical diffraction tomography, the modified
              Newton method, and the pseudo-inverse method.>",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  39,
  number   =  12,
  pages    = "1742--1753",
  month    =  dec,
  year     =  1991,
  keywords = "electromagnetic wave scattering;inverse problems;iterative
              methods;microwave imaging;2-D objects;3-D
              objects;Newton-Kantorovich procedure;TE polarization;TM
              polarisation;complex permittivity;electric field;electromagnetic
              imaging;electromagnetic scattering;inhomogeneous lossy dielectric
              objects;inverse scattering;microwave imaging;moment
              method;numerical method;spatial iterative algorithm;Dielectric
              losses;Image reconstruction;Inverse problems;Iterative
              algorithms;Iterative methods;Moment methods;Nonuniform electric
              fields;Permittivity;Shape;Tellurium"
}

@ARTICLE{Isernia2004,
  title    = "New tools and series for forward and inverse scattering problems
              in lossy media",
  author   = "Isernia, T and Crocco, L and D'Urso, M",
  abstract = "A convenient rewriting of the pertinent integral equation is
              exploited to introduce a new model for two-dimensional
              electromagnetic scattering by dielectric objects in lossy media.
              Exploiting this latter, a new series expansion is introduced to
              solve the forward problem accurately and effectively. The first
              term of such a series coincides, in particular situations, with
              the well-known extended Born approximation. Theoretical tools and
              results are given on the range of applicability and rate of
              convergence of the series, which favorably compares with the
              traditional Born one. These tools allow noticing that the new
              model exhibits a lower {"}degree of nonlinearity{"} with respect
              to parameters embedding dielectric characteristics as compared to
              the traditional model, thus suggesting its exploitation in the
              solution of the inverse problem. Numerical examples assessing
              effectiveness and convenience of the proposed models, tools and
              inversion methods are presented.",
  journal  = "Geoscience and Remote Sensing Letters, IEEE",
  volume   =  1,
  number   =  4,
  pages    = "327--331",
  month    =  oct,
  year     =  2004,
  keywords = "absorbing media;approximation theory;convergence;dielectric
              materials;electromagnetic wave scattering;integral
              equations;inverse problems;2D electromagnetic
              scattering;convergence;degree of nonlinearity;dielectric
              objects;dielectric properties;extended Born approximation;forward
              scattering problem;inverse problem;inverse scattering
              problem;inversion method;lossy media;pertinent integral
              equation;Approximation methods;Biological tissues;Buried object
              detection;Dielectric losses;Electromagnetic
              modeling;Electromagnetic scattering;Integral equations;Inverse
              problems;Microwave imaging;Scattering
              parameters;EM;Electromagnetic;inverse scattering;noninvasive
              diagnostics;scattering;subsurface sensing"
}

@ARTICLE{Hu2009,
  title    = "Simultaneous multifrequency inversion of full-waveform seismic
              data",
  author   = "Hu, W and Abubakar, A and Habashy, T",
  abstract = "We present a simultaneous multifrequency inversion approach for
              seismic data interpretation. This algorithm inverts all frequency
              data components simultaneously. A data-weighting scheme balances
              the contributions from different frequency data components so the
              inversion process does not become dominated by high-frequency
              data components, which produce a velocity image with many
              artifacts. A Gauss-Newton minimization approach achieves a high
              convergence rate and an accurate reconstructed velocity image. By
              introducing a modified adjoint formulation, we can calculate the
              Jacobian matrix efficiently, allowing the material properties in
              the perfectly matched layers (PMLs) to be updated automatically
              during the inversion process. This feature ensures the correct
              behavior of the inversion and implies that the algorithm is
              appropriate for realistic applications where a priori information
              of the background medium is unavailable. Two different
              regularization schemes, an L2 -norm and a weighted L2 -norm
              function, are used in this algorithm for smooth profiles and
              profiles with sharp boundaries, respectively. The regularization
              parameter is determined automatically and adaptively by the
              so-called multiplicative regularization technique. To test the
              algorithm, we implement the inversion to reconstruct the Marmousi
              velocity model using synthetic data generated by the
              finite-difference time-domain code. These numerical simulation
              results indicate that this inversion algorithm is robust in terms
              of starting model and noise suppression. Under some
              circumstances, it is more robust than a traditional sequential
              inversion approach.",
  journal  = "Geophysics",
  volume   =  74,
  number   =  2,
  pages    = "R1--R14",
  year     =  2009
}

@ARTICLE{Hu2007,
  title    = "Application of the nearly perfectly matched layer in acoustic
              wave modeling",
  author   = "Hu, W and Abubakar, A and Habashy, T",
  abstract = "In this work, we successfully applied an alternative formulation
              of the perfectly matched layer (PML), the so-called nearly PML
              (NPML), to acoustic wave propagation modeling. The NPML
              formulation shows great advantages over the standard complex
              stretched coordinate PML. The NPML formulation deviates from the
              standard PML through an inexact variable change, but this fact
              only affects the wave behavior in the NPML layer, which is
              outside the region of interest. The equivalence of the
              wave-absorbing performance between these two PML formulations
              (the standard complex stretched coordinate PML formulation and
              the NPML formulation) in 3D Cartesian coordinates for acoustic
              wave propagation modeling is proved mathematically in this work.
              In time-domain methods, the advantages of the NPML over the
              standard PML were explained by both the analytical analysis and
              the numerical simulations in terms of implementation simplicity
              and computational efficiency. The computation time saving is up
              to 17\% for the 2D example used in this work. For 3D problems,
              this computational saving is more significant. After
              theoretically analyzing the numerical reflections from the NPML
              and the standard PML, we concluded that these two PML
              formulations have exactly the same performance, even after
              spatial discretization. This conclusion is validated by numerical
              experiment. Finally, we tested the NPML in the Marmousi velocity
              model and found its wave-absorbing rate is high enough, even for
              this realistic structure.",
  journal  = "Geophysics",
  volume   =  72,
  number   =  5,
  pages    = "SM169--SM175",
  year     =  2007
}

@ARTICLE{Hu2005,
  title    = "Quasi-three-dimensional method of moments for analyzing
              electromagnetic wave scattering in microwave tomography systems",
  author   = "Hu, Jin-Lin and Wu, Zhipeng and McCann, H and Davis, L E and Xie,
              Cheng-Gang",
  abstract = "A new quasi-three-dimensional method of moments (Quasi-3-D MoM)
              for analyzing electromagnetic wave scattering from a cylindrical
              dielectric object surrounded by a dipole array in microwave
              tomography systems is presented in this paper. A wire-volumetric
              electric field integral equation is derived for the
              electromagnetic wave scattering phenomena in microwave tomography
              systems. The new method is based on the MoM and involves
              rectangular cylindrical cells modeling the cylindrical object.
              The distribution of electric flux densities along the axial
              direction of cylindrical cells is expanded as a Fourier series
              multiplied by an attenuation factor, which is one part of basis
              functions. Therefore, the Quasi-3-D MoM is performed in a
              two-dimensional discretization, and the computational complexity
              is reduced. Detailed mathematical steps along with some numerical
              results are presented to illustrate the efficacy and accuracy of
              this approach.",
  journal  = "IEEE Sens. J.",
  volume   =  5,
  number   =  2,
  pages    = "216--223",
  month    =  apr,
  year     =  2005,
  keywords = "Fourier series;computational complexity;dielectric
              bodies;electric field integral equations;electromagnetic wave
              scattering;method of moments;microwave imaging;tomography;2D
              discretization;Fourier series;attenuation factor;cylindrical
              dielectric object;dipole array;electric flux
              density;electromagnetic wave scattering;microwave tomography
              systems;quasi-3D method of moments;rectangular cylindrical
              cells;wire-volumetric electric field integral
              equation;Attenuation;Dielectrics;Electromagnetic
              analysis;Electromagnetic scattering;Fourier series;Integral
              equations;Microwave antenna arrays;Microwave theory and
              techniques;Moment methods;Tomography;Dielectric object;Fourier
              series;dipole array;electric field integral
              equation;electromagnetic wave scattering;method of moments
              (MoM);microwave tomography"
}

@article{Howard1986,
  title={Synthesis of EM geophysical tomographic data},
  author={Howard, Allen Q and Kretzschmar, JL},
  journal={Proceedings of the IEEE},
  volume={74},
  number={2},
  pages={353--360},
  year={1986},
  publisher={IEEE}
}


@article{Harada2001,
  title={Image reconstruction of a three-dimensional dielectric object using a gradient-based optimization},
  author={Harada, Haruyuki and Tanaka, Mitsuru and Takenaka, Takashi},
  journal={Microwave and Optical Technology Letters},
  volume={29},
  number={5},
  pages={332--336},
  year={2001},
  publisher={Wiley Online Library}
}

@ARTICLE{Harada1995,
  title    = "Conjugate gradient method applied to inverse scattering problem",
  author   = "Harada, H and Wall, D J N and Takenaka, T and Tanaka, M",
  abstract = "A new reconstruction algorithm for diffraction tomography is
              presented. The algorithm is based on the minimization of a
              functional which is defined as the norm of the discrepancy
              between the measured scattering amplitude and the calculated one
              for an estimated object function. By using the conjugate gradient
              method to minimize the functional, one can derive an iterative
              formula for getting the object function. Numerical results for
              some two-dimensional scatterers show that the algorithm is very
              effective in reconstructing refractive index distributions to
              which the first-order Born approximation can not be applied. In
              addition, the number of iterations is reduced by using a priori
              information about the outer boundary of the objects. Furthermore,
              the method is not so sensitive to the presence of noise in the
              scattered field data",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  43,
  number   =  8,
  pages    = "784--792",
  month    =  aug,
  year     =  1995,
  keywords = "conjugate gradient methods;electromagnetic wave
              diffraction;electromagnetic wave scattering;functional
              equations;inverse problems;minimisation;refractive index;signal
              reconstruction;tomography;a priori information;conjugate gradient
              method;diffraction tomography;first-order Born
              approximation;functional;inverse scattering problem;iterative
              formula;minimization;noise;object function;outer
              boundary;reconstruction algorithm;refractive index
              distributions;scattered field data;scattering
              amplitude;two-dimensional scatterers;Amplitude
              estimation;Diffraction;Gradient methods;Inverse
              problems;Iterative algorithms;Iterative methods;Minimization
              methods;Reconstruction algorithms;Scattering;Tomography"
}

@ARTICLE{Haffa1992,
  title    = "The finite difference method for S-parameter calculation of
              arbitrary three-dimensional structures",
  author   = "Haffa, Steffen and Hollmann, Detlev and Wiesbeck, W",
  abstract = "Describes the application of the finite-difference method for the
              determination of scattering parameters of passive, arbitrary
              three-dimensional, lossy structures. Maxwell's equations are
              solved in the frequency domain by solution of a boundary value
              problem. The generalized S-parameters can be computed for any one
              port or two port structure, while dielectric and conductor losses
              are taken into account. Higher order mode coupling can be
              considered and different geometries are allowed at the input and
              output ports. Verification calculations are given and results are
              presented for typical structures",
  journal  = "IEEE Trans. Microw. Theory Tech.",
  volume   =  40,
  number   =  8,
  pages    = "1602--1610",
  month    =  aug,
  year     =  1992,
  keywords = "S-parameters;boundary-value problems;difference
              equations;losses;rectangular waveguides;waveguide
              theory;Maxwell's equations;S-parameter calculation;boundary value
              problem;conductor losses;finite difference method;frequency
              domain;geometries;lossy structures;mode coupling;output
              ports;scattering parameters;three-dimensional structures;two port
              structure;Boundary value problems;Circuits;Conductors;Dielectric
              losses;Finite difference methods;Frequency domain
              analysis;Geometry;Maxwell equations;Scattering parameters;Time
              domain analysis"
}

@ARTICLE{Haddadin1998,
  title       = "Imaging strongly scattering media using a multiple frequency
                 distorted Born iterative method",
  author      = "Haddadin, O S and Ebbini, E S",
  affiliation = "Schlumberger-Doll Res., Ridgefield, CT.",
  abstract    = "The distorted Born iterative (DBI) method is a powerful
                 approach for solving the inverse scattering problem for
                 ultrasound tomographic imaging. This method alternates between
                 solving the inverse scattering problem for the scattering
                 function and the forward scattering problem for the total
                 field and the inhomogeneous Green's function. The algorithm is
                 initialized using the basic Born inverse solution. One
                 fundamental problem is the algorithm diverges for strongly
                 scattering media. This is caused by the limitation of the Born
                 assumption in estimating the initial step of the algorithm. We
                 present a multiple frequency DBI approach to alleviate this
                 problem, thus extending the applicability of the DBI method to
                 the level of dealing with biological tissue. In this multiple
                 frequency approach, a low frequency DBI-based solution, is
                 used to initialize the algorithm at higher frequencies. The
                 low frequency allows convergence of the algorithm to a
                 contrast level that is close to the true level, however, with
                 a poor spatial resolution. The high frequency improves the
                 spatial resolution while preserving convergence because the
                 difference between the true contrast and the initial contrast
                 is relatively small. We present numerical simulations that
                 demonstrate the ability of this method to reconstruct strongly
                 scattering regions.",
  journal     = "IEEE Trans. Ultrason. Ferroelectr. Freq. Control",
  volume      =  45,
  number      =  6,
  pages       = "1485--1496",
  year        =  1998
}

@ARTICLE{Habashy2004,
  title   = "A {GENERAL} {FRAMEWORK} {FOR} {CONSTRAINT} {MINIMIZATION} {FOR}
             {THE} {INVERSION} {OF} {ELECTROMAGNETIC} {MEASUREMENTS}",
  author  = "Habashy, Tarek M and Abubakar, Aria",
  journal = "Prog. Electromagn. Res. B Pier B",
  volume  =  46,
  year    =  2004
}

@article{Habashy1994,
  title={Simultaneous nonlinear reconstruction of two-dimensional permittivity and conductivity},
  author={Habashy, Tarek M and Oristaglio, Michael L and Hoop, Adrianus T},
  journal={Radio Science},
  volume={29},
  number={4},
  pages={1101--1118},
  year={1994},
  publisher={Wiley Online Library}
}


@ARTICLE{Grzegorczyk2012,
  title       = "Fast 3-d tomographic microwave imaging for breast cancer
                 detection",
  author      = "Grzegorczyk, Tomasz M and Meaney, Paul M and Kaufman, Peter A
                 and diFlorio-Alexander, Roberta M and Paulsen, Keith D",
  affiliation = "Delpsi, Newton, MA 02458, USA.",
  abstract    = "Microwave breast imaging (using electromagnetic waves of
                 frequencies around 1 GHz) has mostly remained at the research
                 level for the past decade, gaining little clinical acceptance.
                 The major hurdles limiting patient use are both at the
                 hardware level (challenges in collecting accurate and
                 noncorrupted data) and software level (often plagued by
                 unrealistic reconstruction times in the tens of hours). In
                 this paper we report improvements that address both issues.
                 First, the hardware is able to measure signals down to levels
                 compatible with sub-centimeter image resolution while keeping
                 an exam time under 2 min. Second, the software overcomes the
                 enormous time burden and produces similarly accurate images in
                 less than 20 min. The combination of the new hardware and
                 software allows us to produce and report here the first
                 clinical 3-D microwave tomographic images of the breast. Two
                 clinical examples are selected out of 400+ exams conducted at
                 the Dartmouth Hitchcock Medical Center (Lebanon, NH). The
                 first example demonstrates the potential usefulness of our
                 system for breast cancer screening while the second example
                 focuses on therapy monitoring.",
  journal     = "IEEE Trans. Med. Imaging",
  volume      =  31,
  number      =  8,
  pages       = "1584--1592",
  month       =  aug,
  year        =  2012,
  issn_alt    = "1558-254X"
}

@INPROCEEDINGS{Golnabi2010,
  title     = "Microwave imaging of the breast with incorporated structural
               information",
  booktitle = "{SPIE} Medical Imaging",
  author    = "Golnabi, Amir H and Meaney, Paul M and Geimer, Shireen D and
               Paulsen, Keith D",
  publisher = "International Society for Optics and Photonics",
  pages     = "76260P--76260P--9",
  month     =  "4~" # mar,
  year      =  2010
}

@ARTICLE{Gilmore2009c,
  title    = "Microwave Biomedical Data Inversion Using the {Finite-Difference}
              Contrast Source Inversion Method",
  author   = "Gilmore, C and Abubakar, A and Hu, Wenyi and Habashy, T M and van
              den Berg, P M",
  abstract = "We present a contrast source inversion (CSI) technique which is
              based on a finite-difference (FD) solver for use in microwave
              biomedical imaging. The algorithm is capable of inverting
              complex-permittivity biomedical data sets without the explicit
              use of a forward solver at each iteration. The FD solver is based
              in the frequency domain, utilizes perfectly matched layer (PML)
              boundary conditions, and the stiffness matrix is solved via an LU
              decomposition and Gaussian elimination. An important feature of
              the FD-CSI algorithm is that the stiffness matrix associated with
              the FD solver depends only upon the background medium and
              frequency, and thus the LU decomposition is only performed once,
              before the iterative inversion process. Unlike the usual integral
              equation (IE) based inversion techniques, the FD-CSI algorithm is
              readily capable of utilizing an arbitrary backarbitrary
              backgroundground medium for the inversion process.",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  57,
  number   =  5,
  pages    = "1528--1538",
  month    =  may,
  year     =  2009,
  keywords = "biomedical imaging;finite difference methods;iterative
              methods;permittivity;FD-CSI algorithm;complex
              permittivity;contrast source inversion method;finite-difference
              solver;iterative inversion process;microwave biomedical data
              inversion;microwave biomedical imaging;perfectly matched layer
              boundary conditions;stiffness matrix;Bioinformatics;Biomedical
              imaging;Boundary conditions;Finite difference methods;Frequency
              domain analysis;Integral equations;Iterative algorithms;Matrix
              decomposition;Microwave theory and techniques;Perfectly matched
              layers;Biomedical imaging;electromagnetic fields;inverse
              problems;iterative methods"
}

@ARTICLE{Gilmore2009b,
  title    = "Comparison of an Enhanced Distorted Born Iterative Method and the
              {Multiplicative-Regularized} Contrast Source Inversion method",
  author   = "Gilmore, C and Mojabi, P and LoVetri, J",
  abstract = "For 2D transverse magnetic (TM) microwave inversion,
              multiplicative-regularized contrast source inversion (MR-CSI),
              and the distorted Born iterative method (DBIM) are compared. The
              comparison is based on a computational resource analysis,
              inversion of synthetic data, and inversion of experimentally
              collected data from both the Fresnel and UPC Barcelona data sets.
              All inversion results are blind, but appropriate physical values
              for the reconstructed contrast are maintained. The data sets used
              to test the algorithms vary widely in terms of the background
              media, antennas, and far/near field considerations. To ensure
              that the comparison is replicable, an automatic regularization
              parameter selection method is used for the additive
              regularization within the DBIM, which utilizes a fast
              implementation of the L-curve method and the Laplacian
              regularizer. While not used in the classical DBIM, we introduce
              an MR term to the DBIM in order to provide comparable results to
              MR-CSI. The introduction of this MR term requires only slight
              modifications to the classical DBIM algorithm, and adds little
              computational complexity. The results show that with the addition
              of the MR term in the DBIM, the two algorithms provide very
              similar inversion results, but with the MR-CSI method providing
              advantages for both computational resources and ease of
              implementation.",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  57,
  number   =  8,
  pages    = "2341--2351",
  month    =  aug,
  year     =  2009,
  keywords = "biomedical imaging;inverse problems;biomedical electromagnetic
              imaging;computational complexity;data sets;distorted born
              iterative method;electromagnetic scattering inverse
              problems;multiplicative-regularized contrast source inversion
              method;transverse magnetic microwave;Biology computing;Biomedical
              imaging;Electromagnetic scattering;Image reconstruction;Inverse
              problems;Iterative methods;Magnetic analysis;Microwave
              imaging;Microwave theory and techniques;Testing;Biomedical
              electromagnetic imaging;electromagnetic scattering inverse
              problems;inverse problems"
}

@ARTICLE{Gilmore2009a,
  title   = "Quantitative inversion of complex contrasts with the
             finite-difference contrast source inversion method",
  author  = "Gilmore, Colin and Abubakar, Aria and Hu, Wenyi and Habashy, Tarek
             M and van den Berg, Peter M",
  journal = "2009 IEEE Antennas and Propagation Society International Symposium",
  year    =  2009
}

@ARTICLE{Geffrin2009,
  title    = "Continuing with the Fresnel database: experimental setup and
              improvements in {3D} scattering measurements",
  author   = "Geffrin, J M and Sabouroux, P",
  abstract = "In this paper, the experimental setup and the improvements
              required to obtain further measurements for the third opus of the
              Fresnel Database are presented. The most original feature of
              those new datasets is the fact that they were obtained with
              three-dimensional targets instead of the two-dimensional ones
              used in the two previous opuses. The measurements were performed
              all around the targets under test to collect enough information
              about the objects to be able to perform inversion on their
              scattered fields. As the targets were small in comparison with
              the wavelength, the challenge here was to extract these small
              scattered fields from the measurements, and a specific
              post-processing procedure had to be designed to compensate for
              the drift errors. The five targets selected for the database are
              presented, including the Myster target, a hitherto undivulged
              target that is presented in this paper for the first time, i.e.,
              at the same time as the submissions of all the other contributors
              to this special section. Some scattered field comparisons are
              also presented.",
  journal  = "Inverse Probl.",
  volume   =  25,
  number   =  2,
  pages    = "024001",
  year     =  2009
}

@ARTICLE{Franchois1997,
  title    = "Microwave imaging-complex permittivity reconstruction with a
              {Levenberg-Marquardt} method",
  author   = "Franchois, A and Pichot, C",
  abstract = "This paper refers to quantitative reconstruction of the
              dielectric and conductive property distributions of biological
              objects by means of active microwave imaging. An iterative
              reconstruction algorithm based on the Levenberg-Marquardt method
              is tested with synthetic data. The influence of the receiver
              geometry is investigated and two methods for choosing the
              regularization parameter, an empirical method and generalized
              cross validation (GCV) method, are examined",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  45,
  number   =  2,
  pages    = "203--215",
  month    =  feb,
  year     =  1997,
  keywords = "image reconstruction;iterative methods;medical image
              processing;microwave imaging;microwave
              receivers;permittivity;Levenberg-Marquardt method;active
              microwave imaging;biological objects;complex permittivity
              reconstruction;conductive property distribution;dielectric
              property distribution;empirical method;generalized cross
              validation method;iterative reconstruction algorithm;quantitative
              reconstruction;receiver geometry;regularization
              parameter;synthetic data;Acoustic imaging;Geometry;Image
              reconstruction;Iterative methods;Microwave imaging;Microwave
              theory and techniques;Optical imaging;Permittivity;Reconstruction
              algorithms;X-ray diffraction"
}

@ARTICLE{Franceschini2005,
  title    = "Full-vectorial three-dimensional microwave imaging through the
              iterative multiscaling strategy-a preliminary assessment",
  author   = "Franceschini, G and Franceschini, D and Massa, A",
  abstract = "In this letter, a multiscaling strategy for full-vectorial
              three-dimensional inverse scattering problems is presented. The
              approach is fully iterative, and it avoids solving any forward
              problem at each step. Thanks to the adaptive multiresolution
              model, which offers considerable flexibility for the inclusion of
              the a priori knowledge and of the knowledge acquired during the
              iterative steps of the multiscaling process, the overall
              computational burden as well as the dimension of the search-space
              is considerably reduced. This allows to balance effectively the
              tradeoff between computational costs and achievable resolution
              accuracy. The effectiveness of the proposed approach is
              demonstrated through a selected set of preliminary experiments
              using homogeneous dielectric scatterers in a noisy synthetic
              environment.",
  journal  = "Geoscience and Remote Sensing Letters, IEEE",
  volume   =  2,
  number   =  4,
  pages    = "428--432",
  month    =  oct,
  year     =  2005,
  keywords = "geophysical techniques;inverse problems;microwave imaging;remote
              sensing;adaptive multiresolution model;computational
              costs;full-vectorial 3D microwave imaging;homogeneous dielectric
              scatterers;inverse scattering problems;iterative multiscaling
              strategy;resolution accuracy;search-space;Biomedical
              imaging;Dielectrics;Electromagnetic scattering;Image
              reconstruction;Inverse problems;Iterative methods;Microwave
              imaging;Radar scattering;Rayleigh scattering;Spatial
              resolution;Inverse scattering;iterative multiscaling
              method;microwave imaging;three-dimensional (3-D) geometry"
}


@ARTICLE{Fhager2009,
  title    = "{3D} Image Reconstruction in Microwave Tomography Using an
              Efficient {FDTD} Model",
  author   = "Fhager, A and Padhi, S K and Howard, J",
  abstract = "This letter describes an efficient three-dimensional (3D) image
              reconstruction algorithm for microwave tomography. Using the
              thin-wire approximation with resistive voltage sources (RVS), a
              realistic FDTD model is created for the transmitting and
              receiving antennas. To verify the algorithm, image reconstruction
              is made from experimental data using a cylindrical test object
              made of sunflower oil. In the results, successful image
              reconstruction has been shown, indicating that the FDTD model is
              applicable. For comparison, a reconstruction with a
              two-dimensional (2D) version of the algorithm was made. A
              significant increase in accuracy of the reconstructed object was
              seen for the 3D version.",
  journal  = "IEEE Antennas Wirel. Propag. Lett.",
  volume   =  8,
  pages    = "1353--1356",
  year     =  2009,
  keywords = "finite difference time-domain analysis;image
              reconstruction;microwave imaging;receiving
              antennas;tomography;transmitting antennas;3D image
              reconstruction;FDTD model;cylindrical test object;microwave
              tomography;receiving antennas;resistive voltage sources;sunflower
              oil;thin wire approximation;transmitting antennas;Antenna
              modeling;finite-difference time-domain (FDTD) methods;microwave
              imaging;microwave measurements;tomography"
}

@ARTICLE{Fang2010,
  title       = "Viable {Three-Dimensional} Medical Microwave Tomography:
                 Theory and Numerical Experiments",
  author      = "Fang, Qianqian and Meaney, Paul M and Paulsen, Keith D",
  affiliation = "Martinos Center for Biomedical Imaging, Massachusetts General
                 Hospital (MGH), Charlestown, MA 02129 USA and also with
                 Harvard Medical School, Boston, MA 02115 USA (
                 qianqian.fang.th05@alum.dartmouth.org ).",
  abstract    = "Three-dimensional microwave tomography represents a
                 potentially very important advance over 2D techniques because
                 it eliminates associated approximations which may lead to more
                 accurate images. However, with the significant increase in
                 problem size, computational efficiency is critical to making
                 3D microwave imaging viable in practice. In this paper, we
                 present two 3D image reconstruction methods utilizing 3D
                 scalar and vector field modeling strategies, respectively.
                 Finite element (FE) and finite-difference time-domain (FDTD)
                 algorithms are used to model the electromagnetic field
                 interactions in human tissue in 3D. Image reconstruction
                 techniques previously developed for the 2D problem, such as
                 the dual-mesh scheme, iterative block solver, and adjoint
                 Jacobian method are extended directly to 3D reconstructions.
                 Speed improvements achieved by setting an initial field
                 distribution and utilizing an alternating-direction implicit
                 (ADI) FDTD are explored for 3D vector field modeling. The
                 proposed algorithms are tested with simulated data and
                 correctly recovered the position, size and electrical
                 properties of the target. The adjoint formulation and the FDTD
                 method utilizing initial field estimates are found to be
                 significantly more effective in reducing the computation time.
                 Finally, these results also demonstrate that cross-plane
                 measurements are critical for reconstructing 3D profiles of
                 the target.",
  journal     = "IEEE Trans. Antennas Propag.",
  volume      =  58,
  number      =  2,
  pages       = "449--458",
  month       =  "1~" # feb,
  year        =  2010
}

@ARTICLE{Fang2004,
  title    = "Microwave image reconstruction from {3-D} fields coupled to {2-D}
              parameter estimation",
  author   = "Fang, Q and Meaney, P M and Geimer, S D and Streltsov, A V and
              Paulsen, K D",
  abstract = "An efficient Gauss-Newton iterative imaging technique utilizing a
              three-dimensional (3-D) field solution coupled to a
              two-dimensional (2-D) parameter estimation scheme (3-D/2-D) is
              presented for microwave tomographic imaging in medical
              applications. While electromagnetic wave propagation is described
              fully by a 3-D vector field, a 3-D scalar model has been applied
              to improve the efficiency of the iterative reconstruction process
              with apparently limited reduction in accuracy. In addition, the
              image recovery has been restricted to 2-D but is generalizable to
              three dimensions. Image artifacts related primarily to 3-D
              effects are reduced when compared with results from an entirely
              two- dimensional inversion (2-D/2-D). Important advances in terms
              of improving algorithmic efficiency include use of a block solver
              for computing the field solutions and application of the dual
              mesh scheme and adjoint approach for Jacobian construction.
              Methods which enhance the image quality such as the
              log-magnitude/unwrapped phase minimization were also applied.
              Results obtained from synthetic measurement data show that the
              new 3-D/2-D algorithm consistently outperforms its 2-D/2-D
              counterpart in terms of reducing the effective imaging slice
              thickness in both permittivity and conductivity images over a
              range of inclusion sizes and background medium contrasts.",
  journal  = "IEEE Trans. Med. Imaging",
  volume   =  23,
  number   =  4,
  pages    = "475--484",
  month    =  apr,
  year     =  2004,
  keywords = "Jacobian matrices;image reconstruction;medical image
              processing;microwave imaging;parameter estimation;tomography;2-D
              parameter estimation;3-D field solution;3-D scalar
              model;Gauss-Newton iterative imaging technique;Jacobian
              construction;adjoint method;conductivity image;dual mesh
              scheme;electromagnetic wave propagation;image artifacts;image
              recovery;iterative reconstruction process;log-magnitude phase
              minimization;microwave image reconstruction;microwave tomographic
              imaging;permittivity image;unwrapped phase minimization;Image
              reconstruction;Least squares methods;Medical services;Microwave
              imaging;Microwave theory and techniques;Newton method;Parameter
              estimation;Recursive estimation;Tomography;Two dimensional
              displays;Algorithms;Breast;Humans;Image Enhancement;Image
              Interpretation, Computer-Assisted;Imaging,
              Three-Dimensional;Microwaves;Phantoms, Imaging;Reproducibility of
              Results;Sensitivity and Specificity;Tomography"
}

@article{Estatico2013,
  title={Microwave Imaging of Three-Dimensional Targets by Means of an Inexact-Newton-Based Inversion Algorithm},
  author={Estatico, Claudio and Pastorino, Matteo and Randazzo, Andrea},
  journal={International Journal of Antennas and Propagation},
  volume={2013},
  year={2013},
  publisher={Hindawi Publishing Corporation}
}

@ARTICLE{Duchene2001,
  title    = "Inversion of experimental data using linearized and binary
              specialized nonlinear inversion schemes",
  author   = "Duch\^{e}ne, B",
  abstract = "We deal with an electromagnetic inverse scattering problem where
              the goal is to characterize dielectric and metallic unknown
              targets from measurements of the scattered electric fields that
              result from their interaction with a known interrogating wave in
              the microwave frequency range. This nonlinear and ill-posed
              inverse problem is tackled from experimental data collected in a
              laboratory-controlled experiment led at the Institut Fresnel.
              Inversion is performed by means of the binary modified gradient
              method, a nonlinearized iterative technique tailored to the case
              of homogeneous targets. This method does not always converge
              towards an acceptable solution if initialization of the unknowns
              is not carefully performed. The latter is obtained, herein, from
              diffraction tomography, a linearized solution method which yields
              in a very fast way a rough estimate of the location, shape and
              size of the unknown target.",
  journal  = "Inverse Probl.",
  volume   =  17,
  number   =  6,
  pages    = "1623",
  year     =  2001
}

@ARTICLE{Draine1994,
  title   = "Discrete-dipole approximation for scattering calculations",
  author  = "Draine, Bruce T and Flatau, Piotr J",
  journal = "J. Opt. Soc. Am.",
  volume  =  11,
  number  =  4,
  year    =  1994
}

@ARTICLE{DeZaeytijd2007,
  title    = "{Full-Wave} {Three-Dimensional} Microwave Imaging With a
              Regularized Gauss \#x2013;Newton Method \#x2014; Theory and
              Experiment",
  author   = "De Zaeytijd, J and Franchois, A and Eyraud, C and Geffrin, J-M",
  abstract = "A reconstruction algorithm is detailed for three-dimensional
              full-vectorial microwave imaging based on Newton-type
              optimization. The goal is to reconstruct the three-dimensional
              complex permittivity of a scatterer in a homogeneous background
              from a number of time-harmonic scattered field measurements. The
              algorithm combines a modified Gauss-Newton optimization method
              with a computationally efficient forward solver, based on the
              fast Fourier transform method and the
              marching-on-in-source-position extrapolation procedure. A
              regularized cost function is proposed by applying a
              multiplicative-additive regularization to the least squares
              datafit. This approach mitigates the effect of measurement noise
              on the reconstruction and effectively deals with the
              non-linearity of the optimization problem. It is furthermore
              shown that the modified Gauss-Newton method converges much faster
              than the Broyden-Fletcher-Goldfarb-Shanno quasi-Newton method.
              Promising quantitative reconstructions from both simulated and
              experimental data are presented. The latter data are bi-static
              polarimetric free-space measurements provided by Institut
              Fresnel, Marseille, France.",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  55,
  number   =  11,
  pages    = "3279--3292",
  month    =  nov,
  year     =  2007,
  keywords = "Gaussian processes;Newton method;extrapolation;fast Fourier
              transforms;image reconstruction;microwave
              imaging;Broyden-Fletcher-Gold-farb-Shanno quasi-Newton
              method;Newton-type optimization;fast Fourier transform
              method;full-wave three-dimensional microwave imaging;least
              squares datafit;marching-on-in-source-position extrapolation
              procedure;multiplicative-additive regularization;reconstruction
              algorithm;regularized Gauss-Newton method;regularized cost
              function;three-dimensional complex permittivity;time-harmonic
              scattered field;Gaussian processes;Image reconstruction;Least
              squares methods;Microwave imaging;Microwave theory and
              techniques;Newton method;Permittivity;Reconstruction
              algorithms;Recursive estimation;Scattering;Electromagnetic
              scattering;inverse problems;microwave imaging;optimization
              methods"
}

@article{Chew1994,
  title={A 3D perfectly matched medium from modified Maxwell's equations with stretched coordinates},
  author={Chew, Weng Cho and Weedon, William H},
  journal={Microwave and optical technology letters},
  volume={7},
  number={13},
  pages={599--604},
  year={1994},
  publisher={Wiley Online Library}
}


@article{Chew1990,
  title={Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method},
  author={Chew, WC and Wang, YM},
  journal={Medical Imaging, IEEE Transactions on},
  volume={9},
  number={2},
  pages={218--225},
  year={1990},
  publisher={IEEE}
}

@article{Charbonnier1997,
  title={Deterministic edge-preserving regularization in computed imaging},
  author={Charbonnier, Pierre and Blanc-F{\'e}raud, Laure and Aubert, Gilles and Barlaud, Michel},
  journal={Image Processing, IEEE Transactions on},
  volume={6},
  number={2},
  pages={298--311},
  year={1997},
  publisher={IEEE}
}


@ARTICLE{Catapano2006,
  title    = "A novel effective model for solving {3-D} nonlinear inverse
              scattering problems in lossy scenarios",
  author   = "Catapano, I and Crocco, L and D'Urso, M and Isernia, T",
  abstract = "A proper extension of the contrast source extended Born model,
              recently introduced in the two-dimensional scalar case, is
              proposed to establish a novel full-wave inversion method for
              nonlinear vectorial three-dimensional scattering problems. In
              particular, a suitable auxiliary function, embedding the
              parameters of the unknown targets, is introduced as fundamental
              unknown of the inverse problem instead of the widely used
              contrast function. Numerical examples confirm effectiveness and
              reliability of the proposed inversion approach, which also
              favorably compares with other methods previously known in the
              literature",
  journal  = "Geoscience and Remote Sensing Letters, IEEE",
  volume   =  3,
  number   =  3,
  pages    = "302--306",
  month    =  jul,
  year     =  2006,
  keywords = "absorbing media;geophysical techniques;inverse problems;microwave
              imaging;remote sensing;3D nonlinear inverse scattering
              problem;auxiliary function;extended Born model;Biological
              materials;Electromagnetic scattering;Geometry;Integral
              equations;Inverse problems;Microwave imaging;Microwave theory and
              techniques;Nonlinear equations;Scattering
              parameters;Tomography;Contrast source extended Born inversion
              method;integral equations;inverse scattering;inversion
              methods;microwave tomography;nonlinear inverse problems"
}

@inproceedings{Carfantan1995,
  title={Approche bay{\'e}sienne et algorithme multir{\'e}solution pour un probleme inverse non lin{\'e}aire en tomographie de diffraction},
  author={Carfantan, Herv{\'e} and Mohammad-Djafari, Ali},
  booktitle={15° Colloque sur le traitement du signal et des images, FRA, 1995},
  year={1995},
  organization={GRETSI, Groupe d’Etudes du Traitement du Signal et des Images}
}

@ARTICLE{Carfantan1995a,
  title   = "A Bayesian approach for nonlinear inverse scattering tomographic
             imaging",
  author  = "Carfantan, H and Mohammad-Djafari, A",
  journal = "Proc. IEEE Int. Conf. Acoust. Speech Signal Process.",
  year    =  1995
}

@ARTICLE{Caorsi2004,
  title    = "Microwave medical imaging: potentialities and limitations of a
              stochastic optimization technique",
  author   = "Caorsi, S and Massa, A and Pastorino, M and Rosani, A",
  abstract = "An approach based on a stochastic optimization technique is
              proposed for medical microwave imaging. The approach is based on
              the integral equations of the electromagnetic inverse scattering.
              After discretization of the continuous model, the problem
              solution is recast as a global optimization problem. A functional
              is constructed on the basis of a Markov random field model and
              minimized by a genetic algorithm. In order to reduce the
              computational load, a model of the cross section of the
              biological body is considered. In this way, the investigation
              area is limited by separating the scattering contribution of a
              fixed region under test from those of other parts of the model.
              Some preliminary results concerning a two-dimensional model of a
              human thorax are reported. Such a biological structure is
              inspected by the proposed tomographic approach in order to detect
              and localize the presence of an {"}object{"} modeling a tumor.",
  journal  = "IEEE Trans. Microw. Theory Tech.",
  volume   =  52,
  number   =  8,
  pages    = "1909--1916",
  month    =  aug,
  year     =  2004,
  keywords = "Markov processes;biological tissues;biomedical imaging;genetic
              algorithms;integral equations;microwave imaging;tumours;Markov
              random field model;biological body;biological
              structure;electromagnetic inverse scattering;genetic
              algorithm;global optimization problem;human thorax;integral
              equations;microwave medical imaging;object modeling;stochastic
              optimization;tumor;Biological system modeling;Biomedical
              imaging;Electromagnetic scattering;Genetic algorithms;Integral
              equations;Inverse problems;Markov random fields;Microwave
              imaging;Microwave theory and techniques;Stochastic
              processes;GAs;Genetic algorithms;inverse scattering;medical
              imaging;microwave imaging;optimization problems"
}

@ARTICLE{Caorsi1994,
  title    = "Redundant electromagnetic data for microwave imaging of
              three-dimensional dielectric objects",
  author   = "Caorsi, P and Gragnani, G L and Pastorino, M",
  abstract = "The possibilities of reconstructing the dielectric
              characteristics of unknown three-dimensional dielectric objects
              located inside a known volume are studied by means of numerical
              computer simulations. A numerical approach is proposed that is
              based on the moment method and on the utilization of redundant
              data (i.e., the values of the components of the scattered
              electric field measured outside the investigation volume) in
              order to strictly constrain the solution. In particular, a
              multi-illumination-angle multiview approach is proposed, which is
              based on an integrodifferential formulation of the
              three-dimensional inverse electromagnetic scattering problem. The
              analytical model is discretized using the moment method, and a
              regularization procedure is employed to find a solution, in a
              least-squares sense, to the resulting rectangular ill-conditioned
              linear system of algebraic equations. Since the heaviest
              computations can be performed off line, the computer resources
              required by the approach are entirely independent of the number
              of views. Numerical simulations have been performed to assess the
              effectiveness of the approach in dielectric reconstruction, in
              particular, by evaluating the distortions due to the
              ill-posedness of the inverse-scattering formulation",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  42,
  number   =  5,
  pages    = "581--589",
  month    =  may,
  year     =  1994,
  keywords = "dielectric materials;dielectric properties of
              solids;electromagnetic wave scattering;inverse problems;microwave
              imaging;numerical analysis;3D inverse electromagnetic
              scattering;algebraic equations;analytical model;dielectric
              characteristics;dielectric
              reconstruction;distortions;integrodifferential
              formulation;least-squares;microwave imaging;moment
              method;multi-illumination-angle multiview approach;numerical
              computer simulations;rectangular ill-conditioned linear
              system;redundant electromagnetic data;regularization
              procedure;scattered electric field;three-dimensional dielectric
              objects;Analytical models;Computer simulation;Dielectric
              measurements;Electric variables measurement;Electromagnetic
              measurements;Electromagnetic scattering;Image
              reconstruction;Microwave imaging;Moment methods;Volume
              measurement"
}

@ARTICLE{Caorsi1990,
  title    = "Two-dimensional microwave imaging by a numerical inverse
              scattering solution",
  author   = "Caorsi, S and Gragnani, G L and Pastorino, M",
  abstract = "A numerical approach that aims to detect, by means of
              interrogating microwaves, the locations and the dielectric
              permittivities of unknown inhomogeneous dielectric cylindrical
              objects of arbitrary cross sections that might be present inside
              a fixed area of interest is proposed. An illumination is assumed
              with the electric field vector polarized along the cylindrical
              axis. The two-dimensional Lippman-Schwinger integral equation of
              electromagnetic scattering is transformed into matrix form by the
              moment method. The system obtained is solved by using a
              pseudoinversion algorithm to overcome ill-conditioning problems.
              The first-order Born approximation is also applied when the
              dielectric inhomogeneities are weakly scattering. Computer
              simulations have been performed by means of a numerical program.
              Results show the capabilities and limitations of the proposed
              approach",
  journal  = "IEEE Trans. Microw. Theory Tech.",
  volume   =  38,
  number   =  8,
  pages    = "981--980",
  month    =  aug,
  year     =  1990,
  keywords = "electromagnetic wave scattering;microwave
              imaging;permittivity;dielectric permittivities;electric field
              vector;electromagnetic scattering;first-order Born
              approximation;ill-conditioning problems;inhomogeneous dielectric
              cylindrical objects;numerical inverse scattering
              solution;pseudoinversion algorithm;two-dimensional
              Lippman-Schwinger integral equation;Dielectrics;Electromagnetic
              scattering;Electromagnetic wave polarization;Integral
              equations;Inverse problems;Lighting;Microwave imaging;Nonuniform
              electric fields;Object detection;Permittivity"
}

@article{Byrd1995,
  title={A limited memory algorithm for bound constrained optimization},
  author={Byrd, Richard H and Lu, Peihuang and Nocedal, Jorge and Zhu, Ciyou},
  journal={SIAM Journal on Scientific Computing},
  volume={16},
  number={5},
  pages={1190--1208},
  year={1995},
  publisher={SIAM}
}


@ARTICLE{Bulyshev2004,
  title    = "Three-dimensional vector microwave tomography: theory and
              computational experiments",
  author   = "Bulyshev, A E and Souvorov, A E and Semenov, S Yu and Posukh, V G
              and Sizov, Y E",
  abstract = "Microwave tomography is a new imaging method based on contrast in
              dielectric properties of materials. The mathematical theory of
              microwave tomography involves solving an inverse problem for
              Maxwell's equations. In this paper a new method of solving this
              inverse problem is presented. Based on the known gradient
              approach the method has significant advantages that allow us to
              solve full scale 3D microwave tomographic problems using the
              vector equations. The results of computational experiments are
              presented and discussed. Using simulated and experimental data,
              3D images of mathematical and physical phantoms are obtained. The
              results show the abilities of the method to reveal the internal
              structure of objects in the strong contrast case.",
  journal  = "Inverse Probl.",
  volume   =  20,
  number   =  4,
  pages    = "1239",
  year     =  2004
}

@ARTICLE{Bulyshev2001,
  title       = "Computational modeling of three-dimensional microwave
                 tomography of breast cancer",
  author      = "Bulyshev, A E and Semenov, S Y and Souvorov, A E and Svenson,
                 R H and Nazarov, A G and Sizov, Y E and Tatsis, G P",
  affiliation = "Laser and Applied Technologies Laboratory, Carolinas Medical
                 Center, Charlotte, NC 28203, USA. ssemenov@carolinas.org",
  abstract    = "Microwave tomographic approach is proposed to detect and image
                 breast cancers. Taking into account the big difference in
                 dielectrical properties between normal and malignant tissues,
                 we have proposed using the microwave tomographic method to
                 image a human breast. Because of the anatomical features of
                 the objects, this case has to be referred to the tomography
                 with a limited angle of observation. As a result of computer
                 experiments we have established that multiview cylindrical
                 configurations are able to provide microwave tomograms of the
                 breast with a small size tumor inside. Using the gradient
                 method, we have developed a computer code to create images of
                 the three-dimensional objects in dielectrical properties on
                 microwave frequencies.",
  journal     = "IEEE Trans. Biomed. Eng.",
  volume      =  48,
  number      =  9,
  pages       = "1053--1056",
  month       =  sep,
  year        =  2001
}

@ARTICLE{Bulyshev2000,
  title    = "Three-dimensional microwave tomography. Theory and computer
              experiments in scalar approximation",
  author   = "Bulyshev, Alexander E and Souvorov, Alexandre E and Semenov,
              Serguei Y and Svenson, Robert H and Nazarov, Alexei G and Sizov,
              Yuri E and Tatsis, George P",
  abstract = "The results of computer simulated experiments in
              three-dimensional microwave tomography in scalar approximation
              are presented. The gradient method is employed to solve
              three-dimensional high-contrast microwave tomographic problems. A
              computer model for full-scale three-dimensional imaging has been
              created. Three-dimensional tomographic images of mathematical
              models of the human torso were obtained. Significant differences
              between two-dimensional and three-dimensional cases are
              emphasized. Some illumination schemes which can be applied in the
              three-dimensional case are discussed. A dependence of image
              quality on the number of vertically placed transmitters has been
              demonstrated. The computer simulation showed that
              three-dimensional full-scale human torso dielectrical properties
              images can be produced with acceptable computational time.",
  journal  = "Inverse Probl.",
  volume   =  16,
  number   =  3,
  pages    = "863",
  year     =  2000
}

@ARTICLE{Bozza2009,
  title    = "An Inexact {Newton-Based} Approach to Microwave Imaging Within
              the Contrast Source Formulation",
  author   = "Bozza, G and Pastorino, M",
  abstract = "In this paper an approach to microwave imaging based on an
              inexact-Newton method within the contrast source formulation of
              the inverse scattering problem is considered. In this framework,
              the iteratively linearized equations of the inverse problem are
              solved by means of the regularizing truncated Landweber
              algorithm. This approach allows an effective and robust tool to
              inspect dielectric objects, as it is shown by the reported
              numerical results. Moreover, thanks to the structure of the
              involved integral equations within the contrast source
              formulation, computer memory saving can be obtained with respect
              to the electric field integral equation framework. Finally, the
              proposed method is validated against experimental data, kindly
              provided by the Institute Fresnel, Marseille, France.",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  57,
  number   =  4,
  pages    = "1122--1132",
  month    =  apr,
  year     =  2009,
  keywords = "electric field integral equations;electromagnetic wave
              scattering;iterative methods;microwave imaging;computer memory
              saving;contrast source formulation;dielectric objects;electric
              field integral equation;electromagnetic inverse
              scattering;inexact-Newton method;iteratively linearized
              equations;microwave imaging;truncated Landweber
              algorithm;Dielectrics;Geophysical measurements;Integral
              equations;Inverse problems;Iterative algorithms;Microwave
              imaging;Microwave theory and techniques;Newton
              method;Robustness;Scattering;Electromagnetic inverse
              scattering;Newton methods;contrast source formulation"
}


@ARTICLE{Berenger1994,
  title    = "A perfectly matched layer for the absorption of electromagnetic
              waves",
  author   = "Berenger, Jean-Pierre",
  abstract = "A new technique of free-space simulation has been developed for
              solving unbounded electromagnetic problems with the
              finite-difference time-domain method. Referred to as PML, the new
              technique is based on the use of an absorbing layer especially
              designed to absorb without reflection the electromagnetic waves.
              The first part of the paper presents the theory of the PML
              technique. The second part is devoted to numerical experiments
              and to numerical comparisons with the previously used techniques
              of free-space simulation. These comparisons show that the PML
              technique works better than the others in all cases; using it
              allows us to obtain a higher accuracy in some problems and a
              release of computational requirements in some others.",
  journal  = "J. Comput. Phys.",
  volume   =  114,
  number   =  2,
  pages    = "185--200",
  month    =  oct,
  year     =  1994
}

@ARTICLE{Belkebir2001,
  title   = "Special section: Testing inversion algorithms against experimental
             data",
  author  = "Belkebir, Kamal and Saillard, Marc",
  journal = "Inverse Probl.",
  volume  =  17,
  number  =  6,
  year    =  2001
}

@ARTICLE{Barriere2011,
  title    = "Contrast source inversion method applied to relatively high
              contrast objects",
  author   = "Barri\`{e}re, Paul-Andr\'{e} and Idier, J\'{e}r\^{o}me and
              Laurin, Jean-Jacques and Goussard, Yves",
  abstract = "This paper presents a contrast source inversion method for
              microwave tomography with improved performance with respect to
              the popular multiplicative regularized contrast source inversion
              (MR-CSI) method when the contrast of the object under study is
              relatively high. More precisely, some shortcomings of MR-CSI
              which may prevent it from performing adequately on higher
              contrast objects are outlined. The proposed method does not
              suffer from such shortcomings, but necessitates the tuning of
              parameters. However, a unique set of parameters can be used in a
              wide variety of experimental conditions related to a given
              application. Simple guidelines to determine their values are
              provided.",
  journal  = "Inverse Probl.",
  volume   =  27,
  number   =  7,
  pages    = "075012",
  year     =  2011
}

@ARTICLE{Barriere2010,
  title    = "Fast Solutions of the {2D} Inverse Scattering Problem Based on a
              {TSVD} Approximation of the Internal Field for the Forward Model",
  author   = "Barriere, P and Idier, J and Goussard, Y and Laurin, J",
  abstract = "An alternative formulation of the microwave tomography problem is
              proposed, in order to reduce the computation time of the
              inversion procedure. The well-known multiplicative regularized
              contrast source inversion method is used as reference algorithm.
              Our formulation is based on a truncated singular value
              decomposition of the matrix involved in the most computationally
              intensive operations of the inversion algorithm. After
              theoretical and practical investigation of the behavior of the
              singular values, it is shown that the corresponding approximation
              does not yield any significant degradation of the quality of the
              solutions even for large complex permittivity contrasts, while
              the computation times are reduced by a factor ranging between 1.1
              and 6 with respect to the original method.",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  58,
  number   =  12,
  pages    = "4015--4024",
  month    =  dec,
  year     =  2010,
  keywords = "approximation theory;electromagnetic wave scattering;inverse
              problems;matrix inversion;microwave imaging;singular value
              decomposition;tomography;2D inverse scattering problem;TSVD
              approximation;complex permittivity contrast;forward
              model;internal field;matrix inversion;microwave tomography
              problem;multiplicative regularized contrast source inversion
              method;truncated singular value decomposition;Approximation
              algorithms;Approximation methods;Convolution;Microwave theory and
              techniques;Nonhomogeneous media;Tomography;Contrast source
              inversion;microwave tomography;nonlinear inversion;singular value
              decomposition"
}

@UNPUBLISHED{Barriere2009,
  title         = "On Algorithms Based on Joint Estimation of Currents and
                   Contrast in Microwave Tomography",
  author        = "Barri\`{e}re, Paul-Andr\'{e} and Idier, J\'{e}r\^{o}me and
                   Goussard, Yves and Laurin, Jean-Jacques",
  abstract      = "This paper deals with improvements to the contrast source
                   inversion method which is widely used in microwave
                   tomography. First, the method is reviewed and weaknesses of
                   both the criterion form and the optimization strategy are
                   underlined. Then, two new algorithms are proposed. Both of
                   them are based on the same criterion, similar but more
                   robust than the one used in contrast source inversion. The
                   first technique keeps the main characteristics of the
                   contrast source inversion optimization scheme but is based
                   on a better exploitation of the conjugate gradient
                   algorithm. The second technique is based on a preconditioned
                   conjugate gradient algorithm and performs simultaneous
                   updates of sets of unknowns that are normally processed
                   sequentially. Both techniques are shown to be more efficient
                   than original contrast source inversion.",
  month         =  "29~" # jan,
  year          =  2009,
  archivePrefix = "arXiv",
  primaryClass  = "math.NA",
  eprint        = "0901.4723"
}

@ARTICLE{Barriere2007,
  title   = "3-term optimization criterion for faster inversion in microwave
             tomography",
  author  = "Barriere, P-A and Idier, J and Goussard, Y and Laurin, J-J",
  journal = "2007 4th IEEE International Symposium on Biomedical Imaging: From
             Nano to Macro",
  year    =  2007
}

@ARTICLE{Avdeev2005,
  title   = "{THREE-DIMENSIONAL} {ELECTROMAGNETIC} {MODELLING} {AND}
             {INVERSION} {FROM} {THEORY} {TO} {APPLICATION}",
  author  = "Avdeev, Dmitry B",
  journal = "Surv. Geophys.",
  volume  =  26,
  pages   = "767--799",
  year    =  2005
}

@ARTICLE{Alonso1992,
  title    = "Green's functions analysis of planar circuits in a two-layer
              grounded medium",
  author   = "Alonso-Monferrer, F and Kishk, A A and Glisson, A W",
  abstract = "A moment method analysis of planar circuits in a layered medium
              is developed. The Green's functions of a two-layer grounded
              medium are used in order to take into account the effect of the
              surface wave, coupling, and radiation. Interpolation techniques
              are used to increase computational efficiency. The embedded
              conductors are modeled with triangular patches. Results for
              several configurations, including direct and proximity coupled
              radiators, are in good agreement with measurements and other
              calculations",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  40,
  number   =  6,
  pages    = "690--696",
  month    =  jun,
  year     =  1992,
  keywords = "Green's function methods;antenna theory;integral
              equations;interpolation;microstrip antennas;microwave integrated
              circuits;strip line components;Green's functions
              analysis;computational efficiency;coupling effects;direct coupled
              radiators;embedded conductors;integral
              equation;interpolation;microstrip antennas;microwave integrated
              circuits;moment method analysis;planar circuits;proximity coupled
              radiators;radiation effects;surface wave effects;triangular
              patches;two-layer grounded medium;Application specific integrated
              circuits;Circuit analysis;Coaxial components;Conductors;Coupling
              circuits;Feeds;Green's function methods;Microstrip;Microwave
              integrated circuits;Surface waves"
}

@ARTICLE{Ali2010,
  title    = "{3D} Nonlinear {Super-Resolution} Microwave Inversion Technique
              Using {Time-Domain} Data",
  author   = "Ali, M A and Moghaddam, M",
  abstract = "A nonlinear three-dimensional full-wave inverse scattering method
              using time-domain data and models is presented. It successfully
              reconstructs 3D images of various unknown objects using
              time-domain data. The method uses Born-type iterations and a
              constrained minimization to reconstruct successively improved
              images. The use of time-domain data allows very few transmitters
              and receivers to be used. It is shown that this technique
              achieves super-resolution, namely 0.1 wavelength. The method is
              able to recover contrasts of over 2:1. It can also recover
              objects with minute contrasts of as low as 10\%, thus taking a
              step towards addressing recent findings in the breast cancer
              imaging community, for example, that some breast tumors have only
              a 10\% contrast with respect to the glandular tissues. This
              method could present a promising tool for the early-stage breast
              cancer detection as well as other medical and subsurface imaging
              applications.",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  58,
  number   =  7,
  pages    = "2327--2336",
  month    =  jul,
  year     =  2010,
  keywords = "cancer;electromagnetic wave scattering;image reconstruction;image
              resolution;iterative methods;medical image processing;time-domain
              analysis;3D image reconstruction;3D inverse scattering method;3d
              nonlinear super-resolution;breast cancer detection;breast cancer
              imaging;iterations method;medical imaging;microwave inversion
              technique;receivers;subsurface imaging;time-domain
              data;transmitters;Biomedical imaging;Breast cancer;Breast
              tumors;Cancer detection;Image reconstruction;Inverse
              problems;Microwave theory and techniques;Minimization
              methods;Time domain analysis;Transmitters;3D inverse
              scattering;breast cancer imaging;medical imaging;subsurface
              imaging;super-resolution"
}

@ARTICLE{Agarwal2013,
  title    = "Improving the Performances of the Contrast Source Extended Born
              Inversion Method by Subspace Techniques",
  author   = "Agarwal, K and Song, Rencheng and D'Urso, M and Chen, Xudong",
  abstract = "Subspace techniques have been introduced in the framework of
              contrast source (CS) extended born (CSEB) model, for improving
              its reconstruction capabilities. Two techniques are demonstrated.
              First, a scheme for generating a good initial guess of the
              scatterer profile is shown. Second, subspace-based optimization
              method is used for optimization. Using the suggested techniques,
              CSEB model can be applied for solving inverse electromagnetic
              scattering problem with an extended range of application with
              respect to previous contributions, particularly for very high
              contrast lossy scatterers.",
  journal  = "Geoscience and Remote Sensing Letters, IEEE",
  volume   =  10,
  number   =  2,
  pages    = "391--395",
  month    =  mar,
  year     =  2013,
  keywords = "electromagnetic wave scattering;optimisation;CSEB model;contrast
              source extended born inversion method;high contrast lossy
              scatterer;inverse electromagnetic scattering
              problem;subspace-based optimization method;Computational
              modeling;Cost function;Image reconstruction;Inverse
              problems;Permittivity;Scattering;Contrast source (CS) extended
              born (CSEB) model;high contrast;inverse electromagnetic
              scattering;strong scatterers;subspace optimization method"
}

@ARTICLE{Abubakar2012b,
  title    = "Application of the Multiplicative Regularized Gauss
              \#x2013;Newton Algorithm for {Three-Dimensional} Microwave
              Imaging",
  author   = "Abubakar, A and Habashy, T M and Pan, Guangdong and Li, Mao-Kun",
  abstract = "We apply the so-called multiplicative regularized Gauss-Newton
              inversion algorithm for solving three-dimensional electromagnetic
              microwave inverse problems. This inversion algorithm
              automatically adjusts the regularization parameter and when
              combined with the total variation type regularization function,
              it can provide inversion results with excellent edge-preserving
              characteristics. In addition, in order to deal with an extensive
              memory requirement for the Gauss-Newton method, we employ an
              implicit Jacobian calculation scheme. By using this scheme we do
              not have to explicitly store the Jacobian matrix. Hence, we are
              able to significantly reduce the memory requirement of the
              Gauss-Newton method albeit at an additional computational
              overhead. Furthermore, in order to be able to handle a large
              scale computational problem, both the forward and the inversion
              algorithms are parallelized using the MPI library, where we
              obtain a nearly linear speedup factor. We demonstrate efficiency
              and robustness of this algorithm by inverting synthetic data,
              Fresnel experimental data, and biomedical experimental data.",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  60,
  number   =  5,
  pages    = "2431--2441",
  month    =  may,
  year     =  2012,
  keywords = "Jacobian matrices;Newton method;application program
              interfaces;computational electromagnetics;computerised
              instrumentation;inverse problems;message passing;microwave
              imaging;parallel algorithms;parameter estimation;Jacobian
              matrix;MPI library;edge-preserving characteristics;implicit
              Jacobian calculation scheme;memory requirement
              reduction;multiplicative regularized Gauss-Newton inversion
              algorithm;nearly linear speedup factor;parallel
              algorithms;regularization parameter adjustment;three-dimensional
              electromagnetic microwave inverse problems;three-dimensional
              microwave imaging;total variation type regularization
              function;Computational complexity;Data models;Jacobian
              matrices;Mathematical
              model;Noise;Receivers;Vectors;Electromagnetic;inverse
              problem;microwave;regularization;three-dimensional"
}

@ARTICLE{Abubakar2012a,
  title    = "Microwave Data Inversions Using the {Source-Receiver} Compression
              Scheme",
  author   = "Abubakar, A and Habashy, T M and Pan, Guangdong",
  abstract = "We apply a source-receiver compression approach to reduce the
              computational time and memory usage of the nonlinear inversion
              approaches for interpreting three-dimensional microwave data. By
              detecting and quantifying the extent of redundancy in the data,
              we assemble a reduced set of simultaneous sources and receivers
              that are weighted sums of the physical sources and receivers
              employed in the measurement setup. Because the number of these
              simultaneous sources and receivers can be significantly less than
              those of the physical sources and receivers, the computational
              time and memory usage of any inversion method such as
              steepest-descent, nonlinear conjugate-gradient, contrast-source
              inversion, and quasi-Newton can be tremendously reduced. The
              scheme is based on decomposing the data into their principal
              components using a singular-value decomposition approach and the
              data compression is done through the elimination of eigenvectors
              corresponding to small eigenvalues. Consequently, this will also
              suppress the effect of noise in the data. As a concept
              demonstration we show that this approach has the potential of
              significantly reducing both computational time and memory usage
              of the Gauss-Newton inversion method by few orders of magnitude.",
  journal  = "IEEE Trans. Antennas Propag.",
  volume   =  60,
  number   =  6,
  pages    = "2853--2864",
  month    =  jun,
  year     =  2012,
  keywords = "conjugate gradient methods;data compression;eigenvalues and
              eigenfunctions;inverse problems;microwave imaging;singular value
              decomposition;3D microwave data;Gauss-Newton inversion
              method;computational time;contrast source
              inversion;eigenvectors;memory usage;microwave data
              inversions;noise suppression;nonlinear conjugate
              gradient;physical sources;quasi-Newton method;singular value
              decomposition;source receiver compression scheme;steepest descent
              methods;the data compression;weighted sums;Data
              models;Eigenvalues and eigenfunctions;Equations;Jacobian
              matrices;Mathematical model;Noise
              measurement;Receivers;Compression;electromagnetic;inverse
              problem;microwave;three-dimensional"
}

@ARTICLE{Abubakar2010,
  title   = "Multiplicative regularized {Gauss-Newton} approach for
             three-dimensional microwave imaging",
  author  = "Abubakar, Aria and Habashy, Tarek M",
  journal = "IEEE MTTS Int. Microw. Symp.",
  year    =  2010
}

@ARTICLE{Abubakar2009,
  title    = "Application of the finite-difference contrast-source inversion
              algorithm to seismic full-waveform data",
  author   = "Abubakar, A and Hu, W and Habashy, T and van den Berg, P",
  abstract = "We have applied the finite-difference contrast-source inversion
              (FDCSI) method to seismic full-waveform inversion problems. The
              FDCSI method is an iterative nonlinear inversion algorithm.
              However, unlike the nonlinear conjugate gradient method and the
              Gauss-Newton method, FDCSI does not solve any full forward
              problem explicitly in each iterative step of the inversion
              process. This feature makes the method very efficient in solving
              large-scale computational problems. It is shown that FDCSI, with
              a significant lower computation cost, can produce inversion
              results comparable in quality to those produced by the
              Gauss-Newton method and better than those produced by the
              nonlinear conjugate gradient method. Another attractive feature
              of the FDCSI method is that it is capable of employing an
              inhomogeneous background medium without any extra or special
              effort. This feature is useful when dealing with time-lapse
              inversion problems where the objective is to reconstruct changes
              between the baseline and the monitor model. By using the baseline
              model as the background medium in crosswell seismic monitoring
              problems, high quality time-lapse inversion results are obtained.",
  journal  = "Geophysics",
  volume   =  74,
  number   =  6,
  pages    = "WCC47--WCC58",
  year     =  2009
}

@ARTICLE{Abubakar2008,
  title    = "A finite-difference contrast source inversion method",
  author   = "Abubakar, A and Hu, W and den Berg, P M van and Habashy, T M",
  abstract = "We present a contrast source inversion (CSI) algorithm using a
              finite-difference (FD) approach as its backbone for
              reconstructing the unknown material properties of inhomogeneous
              objects embedded in a known inhomogeneous background medium.
              Unlike the CSI method using the integral equation (IE) approach,
              the FD-CSI method can readily employ an arbitrary inhomogeneous
              medium as its background. The ability to use an inhomogeneous
              background medium has made this algorithm very suitable to be
              used in through-wall imaging and time-lapse inversion
              applications. Similar to the IE-CSI algorithm the unknown
              contrast sources and contrast function are updated alternately to
              reconstruct the unknown objects without requiring the solution of
              the full forward problem at each iteration step in the
              optimization process. The FD solver is formulated in the
              frequency domain and it is equipped with a perfectly matched
              layer (PML) absorbing boundary condition. The FD operator used in
              the FD-CSI method is only dependent on the background medium and
              the frequency of operation, thus it does not change throughout
              the inversion process. Therefore, at least for the
              two-dimensional (2D) configurations, where the size of the
              stiffness matrix is manageable, the FD stiffness matrix can be
              inverted using a non-iterative inversion matrix approach such as
              a Gauss elimination method for the sparse matrix. In this case,
              an LU decomposition needs to be done only once and can then be
              reused for multiple source positions and in successive iterations
              of the inversion. Numerical experiments show that this FD-CSI
              algorithm has an excellent performance for inverting
              inhomogeneous objects embedded in an inhomogeneous background
              medium.",
  journal  = "Inverse Probl.",
  volume   =  24,
  number   =  6,
  pages    = "065004",
  year     =  2008
}

@ARTICLE{Abubakar2007,
  title       = "The diagonalized contrast source inversion approach for
                 elastic wave inversion",
  author      = "Abubakar, Aria and Habashy, Tarek M",
  affiliation = "Schlumberger-Doll Research, Cambridge, MA, USA.
                 aabubakar@slb.com",
  abstract    = "This study focuses on the inverse scattering of objects
                 embedded in a homogeneous elastic background. The medium is
                 probed by ultrasonic sources, and the scattered fields are
                 observed along a receiver array. The goal is to retrieve the
                 shape, location, and constitutive parameters of the objects
                 through an inversion procedure. The problem is formulated
                 using a vector integral equation. As is well-known, this
                 inverse scattering problem is nonlinear and ill-posed. In a
                 realistic configuration, this nonlinear inverse scattering
                 problem involves a large number of unknowns, hence the
                 application of full nonlinear inversion approaches such as
                 Gauss-Newton or nonlinear gradient methods might not be
                 feasible, even with present-day computer power. Hence, in this
                 study we use the so-called diagonalized contrast source
                 inversion (DCSI) method in which the nonlinear problem is
                 approximately transformed into a number of linear problems. We
                 will show that, by using a three-step procedure, the nonlinear
                 inverse problem can be handled at the cost of solving three
                 constrained linear inverse problems. The robustness and
                 efficiency of this approach is illustrated using a number of
                 synthetic examples.",
  journal     = "IEEE Trans. Ultrason. Ferroelectr. Freq. Control",
  volume      =  54,
  number      =  9,
  pages       = "1834--1840",
  month       =  sep,
  year        =  2007
}

@ARTICLE{Abubakar2005a,
  title     = "Application of the multiplicative regularized contrast source
               inversion method on {TM-} and {TE-polarized} experimental
               Fresnel data",
  author    = "Abubakar, Aria and van den Berg, Peter M and Habashy, Tarek M",
  abstract  = "This paper presents the results of profile inversion of
               multi-frequency electromagnetic scattered field data, measured
               by the Institute Fresnel (Marseille, France), from cylindrical
               objects, both for TM and TE illuminations. The reconstructions
               are obtained by applying the multiplicative regularized contrast
               source inversion (MR-CSI) method. Since we are dealing with
               configurations consisting of both dielectric and metallic
               objects, we reconstruct both the permittivity and the
               conductivity of the unknown objects. The results show that the
               MR-CSI method successfully performs 'blind' inversion of a wide
               class of scattered field data.",
  journal   = "Inverse Probl.",
  publisher = "IOP Publishing",
  volume    =  21,
  number    =  6,
  pages     = "S5",
  month     =  "1~" # dec,
  year      =  2005
}


@ARTICLE{Abubakar2005b,
  title    = "The diagonalized contrast source approach: an inversion method
              beyond the Born approximation",
  author   = "Abubakar, Aria and Habashy, Tarek M and den Berg, Peter M van and
              Gisolf, Dries",
  abstract = "This paper deals with the imaging and inversion of the
              constitutive material properties of bounded objects embedded in a
              known background medium. The inversion utilizes measurements of
              the scattered field due to the illumination of the objects by a
              set of known single-frequency wave fields. We present two inverse
              scattering methods that approximately recast the full nonlinear
              inversion into a number of linear inversion steps. The two
              methods are as computationally efficient as the constrained Born
              inversion but provide reconstruction results that are far
              superior and are almost comparable in quality to the ones
              obtained using a full nonlinear iterative inversion. The linear
              inversion steps follow what is referred to as the source-type
              integral equation approach in which the contrast sources are
              inverted for in the first step from the linear data equation. In
              this step, we employ a local (diagonal) approximation of the
              operator that relates the contrast sources to the incident field.
              Once the contrast sources have been determined, the total
              internal wave fields follow from a direct application of the
              object equation. In the third and final step, the contrast
              function is estimated from either the constitutive relation
              (first method) or from solving the data equation again, this time
              in terms of the contrast profile (second method). The
              computational cost required by the first method is comparable to
              that of a constrained Born inversion. With only twice the
              computational cost, the second method invariably gives an almost
              perfect image. We will demonstrate the two methods for a number
              of representative synthetic examples, both in two and three
              dimensions.",
  journal  = "Inverse Probl.",
  volume   =  21,
  number   =  2,
  pages    = "685",
  year     =  2005
}

@ARTICLE{Abubakar2004b,
  title    = "Iterative forward and inverse algorithms based on domain integral
              equations for three-dimensional electric and magnetic objects",
  author   = "Abubakar, Aria and van den Berg, Peter M",
  abstract = "An iterative approach to full vector three-dimensional inverse
              scattering problems, where the unknown objects can have
              conductivity, permittivity and permeability different from the
              known background medium, is discussed. Since this problem
              involves a large number of unknowns, it has to be solved
              effectively and efficiently so that the results can be obtained
              in timely manner. The forward modeling is based on a domain
              integral equation approach formulated in terms of the electric
              and magnetic contrast sources normalized with the characteristic
              impedance of the background medium. Our numerical tests indicate
              that this formulation is prerequisite in order to arrive at a
              forward solution within an acceptable number of iterations, and
              hence it is also of significant importance in the optimization
              process of the inverse problem. The inverse scattering problem is
              attacked using the Multiplicative Regularized Contrast Source
              Inversion method as known in the literature. The complexity of
              this inverse method is approximately equal to the complexity of
              two equivalent forward algorithms of the conjugate gradient type.
              Furthermore, this inverse method has been armed with a weighted
              L2-norm regularizer which has been included as a multiplicative
              constraint. Some representative numerical testings will be
              presented to illustrate the ability of the our numerical
              algorithms.",
  journal  = "J. Comput. Phys.",
  volume   =  195,
  number   =  1,
  pages    = "236--262",
  month    =  "20~" # mar,
  year     =  2004,
  keywords = "Inverse scattering; Three-dimensional; Full-vectorial; Iterative
              technique; Nonlinear problem; Integral equation; Electric and
              magnetic objects"
}

@ARTICLE{Abubakar2004a,
  title    = "A robust iterative method for Born inversion",
  author   = "Abubakar, A and van den Berg, P M and Semenov, S Y",
  abstract = "We present a robust iterative method to solve the inverse
              scattering problem in cases where the Born approximation is
              valid. We formulate this linearized inverse problem in terms of
              the unknown material contrast and the unknown contrast sources
              and we solve the problem by minimizing a cost functional
              consisting of two terms. The first term represents the
              differences between the actual data and the modeled data, while
              the second term represents the misfit in the constitutive
              relations between the contrast sources and the incident fields.
              In each iteration, the contrast sources and the contrast are
              reconstructed alternatingly, using subsequently a conjugate
              gradient step for the contrast source updates and a direct
              inversion of a diagonal matrix for the contrast. A further
              regularization with a multiplicative regularization factor is
              discussed. In this regularization procedure the relative
              variation of the contrast is minimized as well. As a test case we
              consider the two-dimensional (2-D) transverse magnetic
              polarization problem. Synthetic numerical examples are presented
              in order to compare the presented algorithm to the traditional
              Born algorithm. Results with respect to the inversion of
              experimental data are presented as well. In addition, some
              inversion results for the subsurface sensing problem, both in two
              and three dimensions, are presented.",
  journal  = "IEEE Trans. Geosci. Remote Sens.",
  volume   =  42,
  number   =  2,
  pages    = "342--354",
  month    =  feb,
  year     =  2004,
  keywords = "conjugate gradient methods;geophysical techniques;inverse
              problems;iterative methods;remote sensing;2D transverse magnetic
              polarization;Born approximation;Born inversion;conjugate gradient
              step;constitutive relations;contrast sources;cost function
              minimization;diagonal matrix;direct inversion;incident
              fields;inverse scattering problem;linear inversion;linearized
              inverse problem;material contrast;multiplicative regularization
              factor;robust iterative method;Approximation methods;Biomedical
              measurements;Cost function;Electromagnetic scattering;Image
              reconstruction;Inverse problems;Iterative algorithms;Iterative
              methods;Magnetic field measurement;Robustness"
}

@ARTICLE{Abubakar2003,
  title    = "{TWO-} {AND} {THREE-DIMENSIONAL} {ALGORITHMS} {FOR} {MICROWAVE}
              {IMAGING} {AND} {INVERSE} {SCATTERING}",
  author   = "Abubakar, A and van den Berg, P M and Semenov, S Y",
  abstract = "In this paper the Contrast Source Inversion method using a
              multiplicative weighted L2-norm Total Variation regularizer is
              applied to two- and three-dimensional image reconstruction from
              electromagnetic microwave tomography data. This iterative method
              avoids solving a full forward problem in each iteration which
              makes the method suitable to handle a large scale computational
              problem. Numerical results both from simulation and experimental
              data with high contrast biological objects in two- and
              three-dimensional are presented and discussed.",
  journal  = "Journal of Electromagnetic Waves and Applications",
  volume   =  17,
  number   =  2,
  pages    = "209--231",
  year     =  2003
}

@ARTICLE{Abubakar2002,
  title    = "Imaging of biomedical data using a multiplicative regularized
              contrast source inversion method",
  author   = "Abubakar, A and van den Berg, P M and Mallorqui, J J",
  abstract = "In this paper, the recently developed multiplicative regularized
              contrast source inversion method is applied to microwave
              biomedical applications. The inversion method is fully iterative
              and avoids solving any forward problem in each iterative step. In
              this way, the inverse scattering problem can efficiently be
              solved. Moreover, the recently developed multiplicative
              regularizer allows us to apply the method blindly to experimental
              data. We demonstrate inversion from experimental data collected
              by a 2.33-GHz circular microwave scanner using a two-dimensional
              (2-D) TM polarization measurement setup. Further some results of
              a feasibility study of the present inversion method to the 2-D TE
              polarization and the full-vectorial three-dimensional measurement
              will be presented as well",
  journal  = "IEEE Trans. Microw. Theory Tech.",
  volume   =  50,
  number   =  7,
  pages    = "1761--1771",
  month    =  jul,
  year     =  2002,
  keywords = "inverse problems;iterative methods;medical image
              processing;microwave imaging;2.33 GHz;biomedical imaging;circular
              microwave scanner;full-vectorial three-dimensional
              measurement;inverse scattering;iterative method;multiplicative
              regularized contrast source inversion method;two-dimensional TE
              polarization measurement;two-dimensional TM polarization
              measurement;Bioinformatics;Biomedical imaging;Biomedical
              measurements;Inverse problems;Iterative methods;Microwave
              imaging;Microwave measurements;Microwave theory and
              techniques;Polarization;Two dimensional displays"
}

@ARTICLE{Abubakar2001,
  title       = "Total variation as a multiplicative constraint for solving
                 inverse problems",
  author      = "Abubakar, A and van den Berg, P M",
  affiliation = "Centre for Theor. Geosci., Delft Univ. of Technol., Delft, The
                 Netherlands. abubakar@its.tudelft.nl",
  abstract    = "The total variation minimization method for deblurring noise
                 is shown to be effective in increasing the resolution in a
                 contrast source inversion approach to index reconstruction
                 from measured scattered field data. The main drawback is the
                 presence of an artificial weighting parameter in the cost
                 functional, which can only be determined through considerable
                 experimentation Therefore, we introduce the total variation as
                 a multiplicative constraint. Numerical examples demonstrate
                 that the algorithm based on this multiplicative regularization
                 seems to be robust and handling noisy data very well without
                 the necessity of the weighting parameter.",
  journal     = "IEEE Trans. Image Process.",
  volume      =  10,
  number      =  9,
  pages       = "1384--1392",
  year        =  2001
}

@ARTICLE{Abubakar2000,
  title    = "Three-dimensional inverse scattering applied to cross-well
              induction sensors",
  author   = "Abubakar, A and van den Berg, P M",
  abstract = "Cross-well induction logging as known in the oil industry is a
              method for determining the electrical conductivity distribution
              between boreholes from the low-frequency electromagnetic field
              measurements in the boreholes. The authors discuss the
              reconstructions of the three-dimensional (3D) conductivity
              distribution using the contrast source inversion (CSI) method. In
              order to improve the reconstruction results, the concept of the
              extended Born approximation has been used to arrive at a
              preconditioning operator. Results of a number of numerical
              examples show that by using this preconditioning operator, a
              large conductivity contrast of the unknown objects (factor of
              100) can be reconstructed up to an acceptable degree of accuracy.
              Moreover, in each iteration, the computational effort to generate
              the preconditioning operator is negligible",
  journal  = "IEEE Trans. Geosci. Remote Sens.",
  volume   =  38,
  number   =  4,
  pages    = "1669--1681",
  month    =  jul,
  year     =  2000,
  keywords = "geophysical prospecting;geophysical techniques;inverse
              problems;terrestrial electricity;borehole method;contrast source
              inversion method;cross-well induction sensor;electrical
              conductivity;exploration;extended Born approximation;geoelectric
              method;geophysical measurement technique;induction
              logging;inverse problem;low-frequency electromagnetic
              field;preconditioning operator;prospecting;terrestrial
              electricity;tree-dimensional method;Approximation
              methods;Conductivity measurement;Electric variables
              measurement;Electromagnetic measurements;Geologic
              measurements;Green function;Image reconstruction;Inverse
              problems;Iterative methods;Scattering"
}

@MISC{Abubakar1998,
  title = "Abubakar1998.pdf"
}