def mul_wavelet_dec(imArray):
shape = imArray.shape
fig, axes = plt.subplots(2, 4, figsize=[14, 8])
max_lev = 3 # how many levels of decomposition to draw
label_levels = 3 # how many levels to explicitly label on the plots
for level in range(0, max_lev + 1):
if level == 0:
# show the original image before decomposition
axes[0, 0].set_axis_off()
axes[1, 0].imshow(imArray, cmap=plt.cm.gray)
axes[1, 0].set_title('Image')
axes[1, 0].set_axis_off()
continue
# plot subband boundaries of a standard DWT basis
draw_2d_wp_basis(shape,
wavedec2_keys(level),
ax=axes[0, level],
label_levels=label_levels)
axes[0, level].set_title('{} level\ndecomposition'.format(level))
# compute the 2D DWT
c = pywt.wavedec2(imArray, 'haar', mode='periodization', level=level)
# normalize each coefficient array independently for better visibility
c[0] /= np.abs(c[0]).max()
for detail_level in range(level):
c[detail_level +
1] = [d / np.abs(d).max() for d in c[detail_level + 1]]
# show the normalized coefficients
arr, slices = pywt.coeffs_to_array(c)
axes[1, level].imshow(arr, cmap=plt.cm.gray)
axes[1, level].set_title('Coefficients\n({} level)'.format(level))
axes[1, level].set_axis_off()
def dw_show(img):
"""
Code taken from https://pywavelets.readthedocs.io/ to show what wavelet decomposition does.
:param img:
:return:
"""
shape = img.shape
max_lev = 3 # how many levels of decomposition to draw
label_levels = 3 # how many levels to explicitly label on the plots
fig, axes = plt.subplots(2, 4, figsize=[14, 8])
for level in range(0, max_lev + 1):
if level == 0:
# show the original image before decomposition
axes[0, 0].set_axis_off()
axes[1, 0].imshow(img, cmap=plt.cm.gray)
axes[1, 0].set_title('Image')
axes[1, 0].set_axis_off()
continue
# plot subband boundaries of a standard DWT basis
draw_2d_wp_basis(shape,
wavedec2_keys(level),
ax=axes[0, level],
label_levels=label_levels)
axes[0, level].set_title('{} level\ndecomposition'.format(level))
# compute the 2D DWT
c = pywt.wavedec2(img, 'db2', mode='periodization', level=level)
print(level, np.array(c[0]).shape)
# normalize each coefficient array independently for better visibility
c[0] /= np.abs(c[0]).max()
for detail_level in range(level):
c[detail_level +
1] = [d / np.abs(d).max() for d in c[detail_level + 1]]
# show the normalized coefficients
arr, slices = pywt.coeffs_to_array(c)
axes[1, level].imshow(arr, cmap=plt.cm.gray)
axes[1, level].set_title('Coefficients\n({} level)'.format(level))
axes[1, level].set_axis_off()
plt.tight_layout()
plt.show()
x = pywt.data.camera()
shape = x.shape
max_lev = 2
label_levels = 2
fig, axes = plt.subplots(2, 3, figsize=[14, 8])
for level in range(0, max_lev + 1):
if level == 0:
axes[0, 0].set_axis_off()
axes[1, 0].imshow(x, cmap=plt.cm.gray)
axes[1, 0].set_title('Image')
axes[1, 0].set_axis_off()
continue
draw_2d_wp_basis(shape,
wavedec2_keys(level),
ax=axes[0, level],
label_levels=label_levels)
axes[0, level].set_title('{} level\ndecomposition'.format(level))
c = pywt.wavedec2(x, 'db2', mode='periodization', level=level)
c[0] /= np.abs(c[0]).max()
for detail_level in range(level):
c[detail_level +
1] = [d / np.abs(d).max() for d in c[detail_level + 1]]
arr, slices = pywt.coeffs_to_array(c)
axes[1, level].imshow(arr, cmap=plt.cm.gray)
axes[1, level].set_title('Coefficients\n({} level)'.format(level))
axes[1, level].set_axis_off()
plt.tight_layout()
plt.show()
max_lev = 3 # how many levels of decomposition to draw
label_levels = 3 # how many levels to explicitly label on the plots
fig, axes = plt.subplots(2, 4, figsize=[14, 8])
for level in range(0, max_lev + 1):
if level == 0:
# show the original image before decomposition
axes[0, 0].set_axis_off()
axes[1, 0].imshow(x, cmap=plt.cm.gray)
axes[1, 0].set_title('Image')
axes[1, 0].set_axis_off()
continue
# plot subband boundaries of a standard DWT basis
draw_2d_wp_basis(shape, wavedec2_keys(level), ax=axes[0, level],
label_levels=label_levels)
axes[0, level].set_title('{} level\ndecomposition'.format(level))
# compute the 2D DWT
c = pywt.wavedec2(x, 'db2', mode='periodization', level=level)
# normalize each coefficient array independently for better visibility
c[0] /= np.abs(c[0]).max()
for detail_level in range(level):
c[detail_level + 1] = [d/np.abs(d).max() for d in c[detail_level + 1]]
# show the normalized coefficients
arr, slices = pywt.coeffs_to_array(c)
axes[1, level].imshow(arr, cmap=plt.cm.gray)
axes[1, level].set_title('Coefficients\n({} level)'.format(level))
axes[1, level].set_axis_off()
plt.tight_layout()
draw_2d_fswavedecn_basis)
shape = (512, 512)
max_lev = 4 # how many levels of decomposition to draw
label_levels = 2 # how many levels to explicitly label on the plots
if False:
fig, axes = plt.subplots(1, 4, figsize=[16, 4])
axes = axes.ravel()
else:
fig, axes = plt.subplots(2, 2, figsize=[8, 8])
axes = axes.ravel()
# plot a 5-level standard DWT basis
draw_2d_wp_basis(shape, wavedec2_keys(max_lev), ax=axes[0],
label_levels=label_levels)
axes[0].set_title('wavedec2 ({} level)'.format(max_lev))
# plot for the fully separable case
draw_2d_fswavedecn_basis(shape, max_lev, ax=axes[1], label_levels=label_levels)
axes[1].set_title('fswavedecn ({} level)'.format(max_lev))
# get all keys corresponding to a full wavelet packet decomposition
wp_keys = list(product(['a', 'd', 'h', 'v'], repeat=max_lev))
draw_2d_wp_basis(shape, wp_keys, ax=axes[2])
axes[2].set_title('wavelet packet\n(full: {} level)'.format(max_lev))
# plot an example of a custom wavelet packet basis
keys = ['aaaa', 'aaad', 'aaah', 'aaav', 'aad', 'aah', 'aava', 'aavd',
'aavh', 'aavv', 'ad', 'ah', 'ava', 'avd', 'avh', 'avv', 'd', 'h',
'vaa', 'vad', 'vah', 'vav', 'vd', 'vh', 'vv']
shape = (512, 512)
max_lev = 4 # how many levels of decomposition to draw
label_levels = 2 # how many levels to explicitly label on the plots
if False:
fig, axes = plt.subplots(1, 4, figsize=[16, 4])
axes = axes.ravel()
else:
fig, axes = plt.subplots(2, 2, figsize=[8, 8])
axes = axes.ravel()
# plot a 5-level standard DWT basis
draw_2d_wp_basis(shape,
wavedec2_keys(max_lev),
ax=axes[0],
label_levels=label_levels)
axes[0].set_title('wavedec2 ({} level)'.format(max_lev))
# plot for the fully separable case
draw_2d_fswavedecn_basis(shape, max_lev, ax=axes[1], label_levels=label_levels)
axes[1].set_title('fswavedecn ({} level)'.format(max_lev))
# get all keys corresponding to a full wavelet packet decomposition
wp_keys = list(product(['a', 'd', 'h', 'v'], repeat=max_lev))
draw_2d_wp_basis(shape, wp_keys, ax=axes[2])
axes[2].set_title('wavelet packet\n(full: {} level)'.format(max_lev))
# plot an example of a custom wavelet packet basis
keys = [
'aaaa', 'aaad', 'aaah', 'aaav', 'aad', 'aah', 'aava', 'aavd', 'aavh',