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modwt.py
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import numpy as np
import pdb
import pywt
from scipy.ndimage import convolve1d
def upArrow_op(li, j):
if j == 0:
return [1]
N = len(li)
li_n = np.zeros(2**(j - 1) * (N - 1) + 1)
for i in range(N):
li_n[2**(j - 1) * i] = li[i]
return li_n
def period_list(li, N):
n = len(li)
# append [0 0 ...]
n_app = N - np.mod(n, N)
li = list(li)
li = li + [0] * n_app
if len(li) < 2 * N:
return np.array(li)
else:
li = np.array(li)
li = np.reshape(li, [-1, N])
li = np.sum(li, axis=0)
return li
def circular_convolve_mra(h_j_o, w_j):
''' calculate the mra D_j'''
return convolve1d(w_j,
np.flip(h_j_o),
mode="wrap",
origin=(len(h_j_o) - 1) // 2)
def circular_convolve_d(h_t, v_j_1, j):
'''
jth level decomposition
h_t: \tilde{h} = h / sqrt(2)
v_j_1: v_{j-1}, the (j-1)th scale coefficients
return: w_j (or v_j)
'''
N = len(v_j_1)
w_j = np.zeros(N)
ker = np.zeros(len(h_t) * 2**(j - 1))
# make kernel
for i, h in enumerate(h_t):
ker[i * 2**(j - 1)] = h
w_j = convolve1d(v_j_1, ker, mode="wrap", origin=-len(ker) // 2)
return w_j
def circular_convolve_s(h_t, g_t, w_j, v_j, j):
'''
(j-1)th level synthesis from w_j, w_j
see function circular_convolve_d
'''
N = len(v_j)
h_ker = np.zeros(len(h_t) * 2**(j - 1))
g_ker = np.zeros(len(g_t) * 2**(j - 1))
for i, (h, g) in enumerate(zip(h_t, g_t)):
h_ker[i * 2**(j - 1)] = h
g_ker[i * 2**(j - 1)] = g
v_j_1 = np.zeros(N)
v_j_1 = convolve1d(w_j,
np.flip(h_ker),
mode="wrap",
origin=(len(h_ker) - 1) // 2)
v_j_1 += convolve1d(v_j,
np.flip(g_ker),
mode="wrap",
origin=(len(g_ker) - 1) // 2)
return v_j_1
def modwt(x, filters, level):
'''
filters: 'db1', 'db2', 'haar', ...
return: see matlab
'''
# filter
wavelet = pywt.Wavelet(filters)
h = wavelet.dec_hi
g = wavelet.dec_lo
h_t = np.array(h) / np.sqrt(2)
g_t = np.array(g) / np.sqrt(2)
wavecoeff = []
v_j_1 = x
for j in range(level):
w = circular_convolve_d(h_t, v_j_1, j + 1)
v_j_1 = circular_convolve_d(g_t, v_j_1, j + 1)
wavecoeff.append(w)
wavecoeff.append(v_j_1)
return np.vstack(wavecoeff)
def imodwt(w, filters):
''' inverse modwt '''
# filter
wavelet = pywt.Wavelet(filters)
h = wavelet.dec_hi
g = wavelet.dec_lo
h_t = np.array(h) / np.sqrt(2)
g_t = np.array(g) / np.sqrt(2)
level = len(w) - 1
v_j = w[-1]
for jp in range(level):
j = level - jp - 1
v_j = circular_convolve_s(h_t, g_t, w[j], v_j, j + 1)
return v_j
def modwtmra(w, filters):
''' Multiresolution analysis based on MODWT'''
# filter
wavelet = pywt.Wavelet(filters)
h = wavelet.dec_hi
g = wavelet.dec_lo
# D
level, N = w.shape
level = level - 1
D = []
g_j_part = [1]
for j in range(level):
# g_j_part
g_j_up = upArrow_op(g, j)
g_j_part = np.convolve(g_j_part, g_j_up)
# h_j_o
h_j_up = upArrow_op(h, j + 1)
h_j = np.convolve(g_j_part, h_j_up)
h_j_t = h_j / (2**((j + 1) / 2.))
if j == 0: h_j_t = h / np.sqrt(2)
h_j_t_o = period_list(h_j_t, N)
D.append(circular_convolve_mra(h_j_t_o, w[j]))
# S
j = level - 1
g_j_up = upArrow_op(g, j + 1)
g_j = np.convolve(g_j_part, g_j_up)
g_j_t = g_j / (2**((j + 1) / 2.))
g_j_t_o = period_list(g_j_t, N)
S = circular_convolve_mra(g_j_t_o, w[-1])
D.append(S)
return np.vstack(D)
if __name__ == '__main__':
s1 = np.arange(10)
ws = modwt(s1, 'db2', 3)
s1p = imodwt(ws, 'db2')
mra = modwtmra(ws, 'db2')