def wavelets():
M = 7
J = 3
L = 32
filters_set = filter_bank(M, M, J, L=L)
fig, axs = plt.subplots(J,
L,
sharex=True,
sharey=True,
gridspec_kw={
'width_ratios': [1] * L,
'wspace': 0.5,
'hspace': 0.5,
'top': 0.95,
'bottom': 0.05,
'left': 0.1,
'right': 0.95
})
fig.set_figheight(5)
fig.set_figwidth(60)
plt.rc('text', usetex=False)
plt.rc('font', family='serif')
i = 0
func = lambda elems: [(yield f[0][..., 0]) for f in elems]
plot_wavelets(J, L, filters_set['psi'], func)
func = lambda elems: [(yield f[0][..., 1]) for f in elems]
plot_wavelets(J, L, filters_set['psi'], func)
func = lambda elems: [(yield f[1][..., 0]) for f in elems if len(f) > 3]
plot_wavelets(J, L, filters_set['psi'], func)
func = lambda elems: [(yield f[1][..., 1]) for f in elems if len(f) > 3]
plot_wavelets(J, L, filters_set['psi'], func)
func = lambda elems: [(yield f[2][..., 0]) for f in elems if len(f) > 4]
plot_wavelets(J, L, filters_set['psi'], func)
func = lambda elems: [(yield f[2][..., 1]) for f in elems if len(f) > 4]
plot_wavelets(J, L, filters_set['psi'], func)
def main():
M = 32
J = 3
L = 8
filters_set = filter_bank(M, M, J, L=L)
fig, axs = plt.subplots(J, L, sharex=True, sharey=True)
fig.set_figheight(6)
fig.set_figwidth(6)
plt.rc('text', usetex=True)
plt.rc('font', family='serif')
i = 0
for filter in filters_set['psi']:
f_r = filter[0][..., 0].numpy()
f_i = filter[0][..., 1].numpy()
f = f_r + 1j * f_i
filter_c = fft2(f)
filter_c = np.fft.fftshift(filter_c)
axs[i // L, i % L].imshow(colorize(filter_c))
axs[i // L, i % L].axis('off')
axs[i // L,
i % L].set_title("$j = {}$ \n $\\theta={}$".format(i // L, i % L))
i = i + 1
fig.suptitle(
"Wavelets for each scales $j$ and angles $\\theta$ used."
"\n Color saturation and color hue respectively denote complex magnitude and complex phase.",
fontsize=13)
fig.show()
plt.figure()
plt.rc('text', usetex=True)
plt.rc('font', family='serif')
plt.axis('off')
plt.set_cmap('gray_r')
f_r = filters_set['phi'][0][..., 0].numpy()
f_i = filters_set['phi'][0][..., 1].numpy()
f = f_r + 1j * f_i
filter_c = fft2(f)
filter_c = np.fft.fftshift(filter_c)
plt.suptitle(
"The corresponding low-pass filter, also known as scaling function.",
fontsize=13)
filter_c = np.abs(filter_c)
plt.imshow(filter_c)
plt.show()
rot(0.0)
xlocs = np.linspace(-1, 1, num=512)
gaussianExample = f(xlocs, xlocs, .6, .3, np.pi / 6)
mutilated = np.copy(gaussianExample)
nZeros = 12
mutilated[0:nZeros, :] = np.zeros((nZeros, mutilated.shape[1]))
plt.imshow(gaussianExample)
plt.show()
plt.imshow(mutilated)
plt.show()
M = 512
J = 2
L = 7
filters_set = filter_bank(M, M, J, L=L)
transformed = np.zeros((512, 512, len(filters_set['psi'])))
transMut = np.zeros((512, 512, len(filters_set['psi'])))
for i, filter in enumerate(filters_set['psi']):
f_r = filter[0][..., 0].numpy()
f_i = filter[0][..., 1].numpy()
f = f_r + 1j * f_i
transformed[:, :, i] = np.fft.ifft2(fft2(gaussianExample) * f)
transMut[:, :, i] = np.fft.ifft2(fft2(mutilated) * f)
filter0 = filters_set['psi'][2]
filter0 = filter0[0][..., 0].numpy() + 1j * filter0[0][..., 1].numpy()
plt.imshow(abs(filter0))
plt.show()
plt.imshow(transformed[:, :, 4])