4D NUFFT

[stumarcus314]

Are there plans to compute the three types of NUFFT in four dimensions on the CPU and GPU?

[ahbarnett]

Hi Stu, I can safely say we have no such plans this year, and point you to: * a 3-year-old CPU fork with 4D and 5D : https://github.com/palmerb4/finufft5d * various general dim codes, eg in Julia, see here: https://finufft.readthedocs.io/en/latest/related.html What's your application, BTW?

…

On Thu, Jul 10, 2025 at 8:04 PM stumarcus314 ***@***.***> wrote: Are there plans to compute the three types of NUFFT in four dimensions on the CPU and GPU? — Reply to this email directly, view it on GitHub <#712>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ACNZRSW3ZKDKRQGSC2273NT3H35SRAVCNFSM6AAAAACBIMTQ6KVHI2DSMVQWIX3LMV43ERDJONRXK43TNFXW4OZYGU3DKNZQG4> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

-- *-------------------------------------------------------------------~^`^~._.~' |\ Alex Barnett Center for Computational Mathematics, Flatiron Institute | \ http://users.flatironinstitute.org/~ahb 646-876-5942

[stumarcus314]

Thanks a lot for the links. I am interested in joint direction of departure (DoD) and direction of arrival (DoA) estimation for bistatic signals measured by an active sensor array, such as sonars or radars. If the active sensors are arranged on the surface of a 2D manifold, such as the plane or the hemisphere, then each bistatic signal is parameterized in 4D, an azimuth and elevation for the DoD and an azimuth and elevation for the DoA. The signal model is Y = PAS+W, where Y is the measurement matrix, P is a binary down-selection matrix (with unique rows and a single 1 in each row), A is a 4D DFT matrix (where each column represents a candidate DoD-DoA pair), S is a signal amplitude matrix, and W is additive noise. If there are M sensors, N candidate DoD-DoA pairs, where each pair is represented by a 4D parameter, and L snapshots, then Y is MxL, P is MxN, A is NxN, S is NxL, and W is MxL.

I would imagine that the 4D NUFFT would also be useful for modeling problems where measurements are collected as a function of the 3 spatial dimensions (x, y, and z) and time (t).