def fig_5c():
wl_name = 'haar'
lp_d, hp_d, lp_r, hp_r = map(np.array, pywt.Wavelet(wl_name).filter_bank)
num_levels = 2
res = 32
slice = int(res / 2)
p = 0.5
wavelet_slice = generateWavelets(lp_d, hp_d, res, fine=0)
im_vol = np.zeros((res, res, res))
im_vol[slice, :, :] = idwt2(wavelet_slice, lp_r, hp_r, num_levels)
fft_vol = np.fft.fftn(im_vol, axes=(0, 1, 2))
mask = np.random.choice([0, 1], size=(res, res), p=[1 - p, p])
us_fft_vol = np.copy(fft_vol) * 0
print(mask.shape)
for i in range(res):
us_fft_vol[i, :, :] = np.multiply(fft_vol[i, :, :], mask)
ifft_vol = np.fft.ifftn(us_fft_vol, axes=(0, 1, 2))
dwt_slice = dwt2(np.real(ifft_vol[slice, :, :]), lp_d, hp_d, num_levels)
plot3D(np.abs(dwt_slice), title="3D_coarse.png")
def generateWavelets(lp_d, hp_d, _res=100, levels=2, fine=0, padding=0):
img = generateImage(_res)
wv = dwt2(img, lp_d, hp_d, levels)
z = np.zeros((_res + padding, _res + padding))
if fine == 0:
p = int(_res / 4)
z[:p, p:2 * p] = np.abs(wv[:p, p:2 * p])
else:
p = int(_res / 2)
z[p:, p:] = wv[p:, p:]
z = z / np.max(z)
return z
def fig_4_b():
wl_name = 'haar'
lp_d, hp_d, lp_r, hp_r = map(np.array, pywt.Wavelet(wl_name).filter_bank)
num_levels = 2
wv_img1 = generateWavelets(lp_d, hp_d, levels=num_levels, fine=0)
# step 1: IDWT of wavelet domain
iwv_img = idwt2(wv_img1, lp_r, hp_r, levels=num_levels)
# step 2: FFT of image domain
fft_img = np.fft.fft2(iwv_img)
# step 3: random undersampling of FFT domain
us_fft = randomUndersample(fft_img, 0.2)
# step 4: IFFT of undersampled FFT domain
ifft_img = np.real(np.fft.ifft2(us_fft))
# step 5: DWT of image domain
wv_img2 = dwt2(ifft_img, lp_d, hp_d, levels=num_levels)
fig = plt.figure(figsize=plt.figaspect(2 / 3))
X = np.arange(0, 100)
Y = np.arange(0, 100)
X, Y = np.meshgrid(X, Y)
print(wv_img1.shape)
ax = fig.add_subplot(2, 3, 1, projection='3d')
surf = ax.plot_surface(X, Y, wv_img1, color='r')
ax = fig.add_subplot(2, 3, 2, projection='3d')
surf = ax.plot_surface(X, Y, iwv_img, color='r')
ax = fig.add_subplot(2, 3, 3, projection='3d')
surf = ax.plot_surface(X, Y, np.real(np.fft.fftshift(fft_img)), color='r')
ax = fig.add_subplot(2, 3, 6, projection='3d')
surf = ax.plot_surface(X, Y, np.real(np.fft.fftshift(us_fft)), color='r')
ax = fig.add_subplot(2, 3, 5, projection='3d')
surf = ax.plot_surface(X, Y, ifft_img, color='r')
ax = fig.add_subplot(2, 3, 4, projection='3d')
surf = ax.plot_surface(X, Y, wv_img2, color='r')
fig.tight_layout()
fig.savefig("4b_fine.png")
plt.show()
def fig_5a():
wl_name = 'haar'
lp_d, hp_d, lp_r, hp_r = map(np.array, pywt.Wavelet(wl_name).filter_bank)
num_levels = 2
res = 32
slice = int(res / 2)
p = 0.5
mask = np.random.choice([0, 1], size=(res, ), p=[1 - p, p])
mask = np.tile(mask, (res, 1)).T
wavelet_slice = generateWavelets(lp_d, hp_d, res, fine=1)
im_vol = np.zeros((res, res, res))
im_vol[slice, :, :] = idwt2(wavelet_slice, lp_r, hp_r, num_levels)
fft_vol = np.fft.fftn(im_vol, axes=(1, 0))
us_fft_vol = np.copy(fft_vol) * 0
us_fft_vol[slice, :, :] = np.multiply(fft_vol[slice, :, :], mask)
ifft_vol = np.fft.ifftn(us_fft_vol, axes=(1, 0))
dwt_slice = dwt2(np.real(ifft_vol[slice, :, :]), lp_d, hp_d, num_levels)
plot3D(np.abs(dwt_slice), "Single_slice_coarse")