def test_dwt_coeff_len():
x = np.array([3, 7, 1, 1, -2, 5, 4, 6])
w = pywt.Wavelet("sym3")
ln_modes = [pywt.dwt_coeff_len(len(x), w.dec_len, mode) for mode in pywt.Modes.modes]
assert_allclose(ln_modes, [6, 6, 6, 6, 6, 6, 4])
ln_modes = [pywt.dwt_coeff_len(len(x), w, mode) for mode in pywt.Modes.modes]
assert_allclose(ln_modes, [6, 6, 6, 6, 6, 6, 4])
def compose_wvlt_from_vec(pin, imshape, wavelet='db4', mode='symmetric'):
#currently limited to square geometry
w = pywt.Wavelet(wavelet)
Nl = pywt.dwt_max_level(max(imshape), w.dec_len)
levlens = [pywt.dwt_coeff_len(max(imshape), w.dec_len, mode=mode)]
for j in range(1, Nl):
levlens.append(pywt.dwt_coeff_len(levlens[-1], w.dec_len, mode=mode))
levlens.append(levlens[-1])
levlens = levlens[::-1]
p_wvlt = [
reshape(array(pin[0:levlens[0]**2], float), (levlens[0], levlens[0]))
]
celem = levlens[0]**2
for j in range(1, Nl + 1):
t1 = reshape(array(pin[celem:celem + levlens[j]**2], float),
(levlens[j], levlens[j]))
celem += levlens[j]**2
t2 = reshape(array(pin[celem:celem + levlens[j]**2], float),
(levlens[j], levlens[j]))
celem += levlens[j]**2
t3 = reshape(array(pin[celem:celem + levlens[j]**2], float),
(levlens[j], levlens[j]))
celem += levlens[j]**2
p_wvlt.append((t1, t2, t3))
return p_wvlt
def test_dwt_coeff_len():
x = np.array([3, 7, 1, 1, -2, 5, 4, 6])
w = pywt.Wavelet('sym3')
ln = pywt.dwt_coeff_len(data_len=len(x), filter_len=w.dec_len, mode='sym')
assert_(ln == 6)
ln_modes = [pywt.dwt_coeff_len(len(x), w.dec_len, mode) for mode in
pywt.MODES.modes]
assert_allclose(ln_modes, [6, 6, 6, 6, 6, 4])
def test_dwt_coeff_len():
x = np.array([3, 7, 1, 1, -2, 5, 4, 6])
w = pywt.Wavelet('sym3')
ln_modes = [pywt.dwt_coeff_len(len(x), w.dec_len, mode) for mode in
pywt.Modes.modes]
assert_allclose(ln_modes, [6, 6, 6, 6, 6, 4])
ln_modes = [pywt.dwt_coeff_len(len(x), w, mode) for mode in
pywt.Modes.modes]
assert_allclose(ln_modes, [6, 6, 6, 6, 6, 4])
def test_dwt_coeff_len():
x = np.array([3, 7, 1, 1, -2, 5, 4, 6])
w = pywt.Wavelet('sym3')
ln = pywt.dwt_coeff_len(data_len=len(x), filter_len=w.dec_len, mode='sym')
assert_(ln == 6)
ln_modes = [
pywt.dwt_coeff_len(len(x), w.dec_len, mode)
for mode in pywt.MODES.modes
]
assert_allclose(ln_modes, [6, 6, 6, 6, 6, 4])
def test_dwt_coeff_len():
x = np.array([3, 7, 1, 1, -2, 5, 4, 6])
w = pywt.Wavelet('sym3')
ln_modes = [pywt.dwt_coeff_len(len(x), w.dec_len, mode) for mode in
pywt.Modes.modes]
expected_result = [6, ] * len(pywt.Modes.modes)
expected_result[pywt.Modes.modes.index('periodization')] = 4
assert_allclose(ln_modes, expected_result)
ln_modes = [pywt.dwt_coeff_len(len(x), w, mode) for mode in
pywt.Modes.modes]
assert_allclose(ln_modes, expected_result)
def test_dwt_coeff_len():
x = np.array([3, 7, 1, 1, -2, 5, 4, 6])
w = pywt.Wavelet('sym3')
ln_modes = [pywt.dwt_coeff_len(len(x), w.dec_len, mode) for mode in
pywt.Modes.modes]
expected_result = [6, ] * len(pywt.Modes.modes)
expected_result[pywt.Modes.modes.index('periodization')] = 4
assert_allclose(ln_modes, expected_result)
ln_modes = [pywt.dwt_coeff_len(len(x), w, mode) for mode in
pywt.Modes.modes]
assert_allclose(ln_modes, expected_result)
def full_coeff_len(datalen, filtlen, mode):
max_level = pywt.dwt_max_level(datalen, filtlen)
total_len = 0
for i in xrange(max_level):
datalen = pywt.dwt_coeff_len(datalen, filtlen, mode)
total_len += datalen
return total_len + datalen
def __init__(self, depth, init_wavelet, scales, p_drop=0.5):
super().__init__()
print("wavelet dropout:", p_drop)
self.scales = scales
self.wavelet = init_wavelet
self.mode = "zero"
self.coefficient_len_lst = [depth]
for _ in range(scales):
self.coefficient_len_lst.append(
pywt.dwt_coeff_len(
self.coefficient_len_lst[-1],
init_wavelet.dec_lo.shape[-1],
self.mode,
))
self.coefficient_len_lst = self.coefficient_len_lst[1:]
self.coefficient_len_lst.append(self.coefficient_len_lst[-1])
wave_depth = np.sum(self.coefficient_len_lst)
self.depth = depth
self.diag_vec_s = Parameter(
torch.from_numpy(np.ones(depth, np.float32)))
self.diag_vec_g = Parameter(
torch.from_numpy(np.ones(wave_depth, np.float32)))
self.diag_vec_b = Parameter(
torch.from_numpy(np.ones(depth, np.float32)))
perm = np.random.permutation(np.eye(wave_depth, dtype=np.float32))
self.perm = Parameter(torch.from_numpy(perm), requires_grad=False)
self.drop_s = torch.nn.Dropout(p=p_drop)
self.drop_g = torch.nn.Dropout(p=p_drop)
self.drop_b = torch.nn.Dropout(p=p_drop)
def func_IDWT(I_W, level=LEVEL, wavelet=BIOR, mode=MODE):
'''
小波逆变换，将输入的小波参数，根据小波变换等级，小波类型，变换模式将小波参数逆变换为原图像
IDWT
I_W : numpy array
level : wavelet level
wavelet : wavelet type
mode : wavelet mode
'''
width = I_W.shape[0]
height = I_W.shape[0]
S = [-1] * level
current_size = width
for i in range(level):
current_size = pywt.dwt_coeff_len(current_size, pywt.Wavelet(BIOR),
MODE)
S[i] = current_size
S.reverse()
for current_size in S:
# current_size = S[i]
LL = I_W[0:current_size, 0:current_size]
LH = I_W[0:current_size, current_size:2 * current_size]
HL = I_W[current_size:2 * current_size, 0:current_size]
HH = I_W[current_size:2 * current_size, current_size:2 * current_size]
coeffs = [LL, [LH, HL, HH]]
I_W[0:2 * current_size,
0:2 * current_size] = pywt.idwt2(coeffs, wavelet, MODE)
return I_W
def compose_vec_from_wvlt(p_wvlt,imshape,wavelet='db4',mode='symmetric'):
#currently limited to square geometry
w=pywt.Wavelet(wavelet)
Nl=pywt.dwt_max_level(max(imshape),w.dec_len)
levlens=[pywt.dwt_coeff_len(max(imshape),w.dec_len,mode=mode)]
for j in range(1,Nl):
levlens.append( pywt.dwt_coeff_len(levlens[-1],w.dec_len,mode=mode) )
levlens.append(levlens[-1])
levlens=levlens[::-1]
Na=sum(levlens)
ret_arr = empty( (Na*Na,),float)
ret_arr[0:levlens[0]**2] = ravel(p_wvlt[0])
celem=levlens[0]**2
for j in range(1,Nl+1):
for k in range(3):
ret_arr[celem:celem+levlens[j]**2]=ravel(p_wvlt[j][k])
celem+=levlens[j]**2
return ret_arr
def compose_vec_from_wvlt(p_wvlt, imshape, wavelet='db4', mode='symmetric'):
#currently limited to square geometry
w = pywt.Wavelet(wavelet)
Nl = pywt.dwt_max_level(max(imshape), w.dec_len)
levlens = [pywt.dwt_coeff_len(max(imshape), w.dec_len, mode=mode)]
for j in range(1, Nl):
levlens.append(pywt.dwt_coeff_len(levlens[-1], w.dec_len, mode=mode))
levlens.append(levlens[-1])
levlens = levlens[::-1]
Na = sum(levlens)
ret_arr = empty((Na * Na, ), float)
ret_arr[0:levlens[0]**2] = ravel(p_wvlt[0])
celem = levlens[0]**2
for j in range(1, Nl + 1):
for k in range(3):
ret_arr[celem:celem + levlens[j]**2] = ravel(p_wvlt[j][k])
celem += levlens[j]**2
return ret_arr
def full_coeff_len(datalen, filtlen, mode):
max_level = wt.dwt_max_level(datalen, filtlen)
total_len = 0
for i in xrange(max_level):
datalen = wt.dwt_coeff_len(datalen, filtlen, mode)
total_len += datalen
return total_len + datalen
def compose_wvlt_from_vec(pin,imshape,wavelet='db4',mode='symmetric'):
#currently limited to square geometry
w=pywt.Wavelet(wavelet)
Nl=pywt.dwt_max_level(max(imshape),w.dec_len)
levlens=[pywt.dwt_coeff_len(max(imshape),w.dec_len,mode=mode)]
for j in range(1,Nl):
levlens.append( pywt.dwt_coeff_len(levlens[-1],w.dec_len,mode=mode) )
levlens.append(levlens[-1])
levlens=levlens[::-1]
p_wvlt=[reshape(array(pin[0:levlens[0]**2],float),(levlens[0],levlens[0]))]
celem=levlens[0]**2
for j in range(1,Nl+1):
t1=reshape(array(pin[celem:celem+levlens[j]**2],float),(levlens[j],levlens[j]))
celem+=levlens[j]**2
t2=reshape(array(pin[celem:celem+levlens[j]**2],float),(levlens[j],levlens[j]))
celem+=levlens[j]**2
t3=reshape(array(pin[celem:celem+levlens[j]**2],float),(levlens[j],levlens[j]))
celem+=levlens[j]**2
p_wvlt.append( (t1,t2,t3) )
return p_wvlt
def compute_coeff_no(self, init_length):
"""
Compute the number of resulting wavelet coefficients.
@param init_length: length of the input signal vector.
"""
lengths = [init_length]
for J in range(self.scales):
lengths.append(
pywt.dwt_coeff_len(lengths[-1], self.dec_lo.shape[-1],
self.mode))
lengths.append(lengths[-1])
return lengths[1:]
def wavelet_BSS(data):
raw = data
tp,channels = raw.shape
wv = pywt.Wavelet('dmey')
reduced_tp = int(pywt.dwt_coeff_len(data_len=tp, filter_len=wv.dec_len, mode='symmetric'))
WT = np.zeros((reduced_tp,channels-1))
#coeff = np.zeros((22)) #coeffcients from wavelet transformation
coeff = np.zeros((reduced_tp,channels-1))
for c in range(channels-1): #exclude the markers
A,B = wavelet_trans(raw[:,c],wv)
WT[:,c] = A
#coeff[c] = B
coeff[:,c] = B
n=19 #general neurology techniques say to keep as many channels as possible
#Essentially, remove the noisiest channel
#The remaining channels will be cleaned
#
Z = WT #Define source space as wavelet data
ica = FastICA(n_components = n-1,whiten=True) #use all components but one
Z_ = ica.fit_transform(Z) #Estimated Source Space
A_ = ica.mixing_ #Retrieve estimated mixing matrix with reduced dimension
W_p = np.linalg.pinv(A_) #forced inverse of modified mixing matrix is the unmixing matrix
#X_filt = np.matmul(Z_,A_)
####create cleaned stack with outlier_detection####
weights = np.zeros((reduced_tp,Z_.shape[1]))
stacks = np.zeros((reduced_tp,Z_.shape[1]))
for c_ in range(Z_.shape[1]):
inp = Z_[:,c_]
weights[:,c_],stacks[:,c_] = outlier_detection(inp)
stacks = robust_referencing(stacks,weights)
cleaned_Z_ = stacks.reshape((Z_.shape[0],Z_.shape[1]))
inv_cleaned_Z_ = ica.inverse_transform(cleaned_Z_)
inv_wavelet_cleaned_ica = np.zeros((tp,channels-1))
for c in range(channels-1): #exclude the markers
cA = inv_cleaned_Z_[:,c]
cD = coeff[:,c]
inv_data = inverse_wavelet(cA,cD)
inv_wavelet_cleaned_ica[:,c] = inv_data
return inv_wavelet_cleaned_ica;
def quad_afb2d(x, cols, rows, mode='zero', split=True, stride=2):
""" Does a single level 2d wavelet decomposition of an input. Does separate
row and column filtering by two calls to
:py:func:`pytorch_wavelets.dwt.lowlevel.afb1d`
Inputs:
x (torch.Tensor): Input to decompose
filts (list of ndarray or torch.Tensor): If a list of tensors has been
given, this function assumes they are in the right form (the form
returned by
:py:func:`~pytorch_wavelets.dwt.lowlevel.prep_filt_afb2d`).
Otherwise, this function will prepare the filters to be of the right
form by calling
:py:func:`~pytorch_wavelets.dwt.lowlevel.prep_filt_afb2d`.
mode (str): 'zero', 'symmetric', 'reflect' or 'periodization'. Which
padding to use. If periodization, the output size will be half the
input size. Otherwise, the output size will be slightly larger than
half.
"""
x = x / 2
C = x.shape[1]
cols = torch.cat([cols] * C, dim=0)
rows = torch.cat([rows] * C, dim=0)
if mode == 'per' or mode == 'periodization':
# Do column filtering
L = cols.shape[2]
L2 = L // 2
if x.shape[2] % 2 == 1:
x = torch.cat((x, x[:, :, -1:]), dim=2)
N2 = x.shape[2] // 2
x = roll(x, -L2, dim=2)
pad = (L - 1, 0)
lohi = F.conv2d(x, cols, padding=pad, stride=(stride, 1), groups=C)
lohi[:, :, :L2] = lohi[:, :, :L2] + lohi[:, :, N2:N2 + L2]
lohi = lohi[:, :, :N2]
# Do row filtering
L = rows.shape[3]
L2 = L // 2
if lohi.shape[3] % 2 == 1:
lohi = torch.cat((lohi, lohi[:, :, :, -1:]), dim=3)
N2 = x.shape[3] // 2
lohi = roll(lohi, -L2, dim=3)
pad = (0, L - 1)
w = F.conv2d(lohi, rows, padding=pad, stride=(1, stride), groups=8 * C)
w[:, :, :, :L2] = w[:, :, :, :L2] + w[:, :, :, N2:N2 + L2]
w = w[:, :, :, :N2]
elif mode == 'zero':
# Do column filtering
N = x.shape[2]
L = cols.shape[2]
outsize = pywt.dwt_coeff_len(N, L, mode='zero')
p = 2 * (outsize - 1) - N + L
# Sadly, pytorch only allows for same padding before and after, if
# we need to do more padding after for odd length signals, have to
# prepad
if p % 2 == 1:
x = F.pad(x, (0, 0, 0, 1))
pad = (p // 2, 0)
# Calculate the high and lowpass
lohi = F.conv2d(x, cols, padding=pad, stride=(stride, 1), groups=C)
# Do row filtering
N = lohi.shape[3]
L = rows.shape[3]
outsize = pywt.dwt_coeff_len(N, L, mode='zero')
p = 2 * (outsize - 1) - N + L
if p % 2 == 1:
lohi = F.pad(lohi, (0, 1, 0, 0))
pad = (0, p // 2)
w = F.conv2d(lohi, rows, padding=pad, stride=(1, stride), groups=8 * C)
elif mode == 'symmetric' or mode == 'reflect':
# Do column filtering
N = x.shape[2]
L = cols.shape[2]
outsize = pywt.dwt_coeff_len(N, L, mode=mode)
p = 2 * (outsize - 1) - N + L
x = mypad(x, pad=(0, 0, p // 2, (p + 1) // 2), mode=mode)
lohi = F.conv2d(x, cols, stride=(stride, 1), groups=C)
# Do row filtering
N = lohi.shape[3]
L = rows.shape[3]
outsize = pywt.dwt_coeff_len(N, L, mode=mode)
p = 2 * (outsize - 1) - N + L
lohi = mypad(lohi, pad=(p // 2, (p + 1) // 2, 0, 0), mode=mode)
w = F.conv2d(lohi, rows, stride=(1, stride), groups=8 * C)
else:
raise ValueError("Unkown pad type: {}".format(mode))
y = w.view((w.shape[0], C, 4, 4, w.shape[-2], w.shape[-1]))
yl = y[:, :, :, 0]
yh = y[:, :, :, 1:]
deg75r, deg105i = pm(yh[:, :, 0, 0], yh[:, :, 3, 0])
deg105r, deg75i = pm(yh[:, :, 1, 0], yh[:, :, 2, 0])
deg15r, deg165i = pm(yh[:, :, 0, 1], yh[:, :, 3, 1])
deg165r, deg15i = pm(yh[:, :, 1, 1], yh[:, :, 2, 1])
deg135r, deg45i = pm(yh[:, :, 0, 2], yh[:, :, 3, 2])
deg45r, deg135i = pm(yh[:, :, 1, 2], yh[:, :, 2, 2])
yhr = torch.stack((deg15r, deg45r, deg75r, deg105r, deg135r, deg165r),
dim=1)
yhi = torch.stack((deg15i, deg45i, deg75i, deg105i, deg135i, deg165i),
dim=1)
yh = torch.stack((yhr, yhi), dim=-1)
yl_rowa = torch.stack((yl[:, :, 1], yl[:, :, 0]), dim=-1)
yl_rowb = torch.stack((yl[:, :, 3], yl[:, :, 2]), dim=-1)
yl_rowa = yl_rowa.view(yl.shape[0], C, yl.shape[-2], yl.shape[-1] * 2)
yl_rowb = yl_rowb.view(yl.shape[0], C, yl.shape[-2], yl.shape[-1] * 2)
z = torch.stack((yl_rowb, yl_rowa), dim=-2)
yl = z.view(yl.shape[0], C, yl.shape[-2] * 2, yl.shape[-1] * 2)
return yl.contiguous(), yh
def quad_afb2d_nonsep(x, filts, mode='zero'):
""" Does a 1 level 2d wavelet decomposition of an input. Doesn't do separate
row and column filtering.
Inputs:
x (torch.Tensor): Input to decompose
filts (list or torch.Tensor): If a list is given, should be the low and
highpass filter banks. If a tensor is given, it should be of the
form created by
:py:func:`pytorch_wavelets.dwt.lowlevel.prep_filt_afb2d_nonsep`
mode (str): 'zero', 'symmetric', 'reflect' or 'periodization'. Which
padding to use. If periodization, the output size will be half the
input size. Otherwise, the output size will be slightly larger than
half.
"""
C = x.shape[1]
Ny = x.shape[2]
Nx = x.shape[3]
# Check the filter inputs
f = torch.cat([filts] * C, dim=0)
Ly = f.shape[2]
Lx = f.shape[3]
if mode == 'periodization' or mode == 'per':
if x.shape[2] % 2 == 1:
x = torch.cat((x, x[:, :, -1:]), dim=2)
Ny += 1
if x.shape[3] % 2 == 1:
x = torch.cat((x, x[:, :, :, -1:]), dim=3)
Nx += 1
pad = (Ly - 1, Lx - 1)
stride = (2, 2)
x = roll(roll(x, -Ly // 2, dim=2), -Lx // 2, dim=3)
y = F.conv2d(x, f, padding=pad, stride=stride, groups=C)
y[:, :, :Ly // 2] += y[:, :, Ny // 2:Ny // 2 + Ly // 2]
y[:, :, :, :Lx // 2] += y[:, :, :, Nx // 2:Nx // 2 + Lx // 2]
y = y[:, :, :Ny // 2, :Nx // 2]
elif mode == 'zero' or mode == 'symmetric' or mode == 'reflect':
# Calculate the pad size
out1 = pywt.dwt_coeff_len(Ny, Ly, mode=mode)
out2 = pywt.dwt_coeff_len(Nx, Lx, mode=mode)
p1 = 2 * (out1 - 1) - Ny + Ly
p2 = 2 * (out2 - 1) - Nx + Lx
if mode == 'zero':
# Sadly, pytorch only allows for same padding before and after, if
# we need to do more padding after for odd length signals, have to
# prepad
if p1 % 2 == 1 and p2 % 2 == 1:
x = F.pad(x, (0, 1, 0, 1))
elif p1 % 2 == 1:
x = F.pad(x, (0, 0, 0, 1))
elif p2 % 2 == 1:
x = F.pad(x, (0, 1, 0, 0))
# Calculate the high and lowpass
y = F.conv2d(x, f, padding=(p1 // 2, p2 // 2), stride=2, groups=C)
elif mode == 'symmetric' or mode == 'reflect':
pad = (p2 // 2, (p2 + 1) // 2, p1 // 2, (p1 + 1) // 2)
x = mypad(x, pad=pad, mode=mode)
y = F.conv2d(x, f, stride=2, groups=C)
else:
raise ValueError("Unkown pad type: {}".format(mode))
y = y.reshape((y.shape[0], C, 4, y.shape[-2], y.shape[-1]))
yl = y[:, :, 0].contiguous()
yh = y[:, :, 1:].contiguous()
return yl, yh
haar = pywt.Wavelet('haar')
db = pywt.Wavelet('db2')
# returns [decomposition, reconstruction] x [low, high]
# reconstruction seem to be the ones i'm familiar with
haar.filter_bank
scale_vals, wavelet_vals, x_vals = haar.wavefun()
plt.plot(x_vals, scale_vals)
plt.show()
plt.plot(x_vals, wavelet_vals)
plt.show()
# length of the coefficients
print pywt.dwt_coeff_len(x.shape[0], haar, "sym")
print pywt.dwt_coeff_len(8, 2, "sym")
# Maximum useful level of decomposition for
# This is currently logged as a bug
print pywt.dwt_max_level(x.shape[0], haar.dec_len)
coeffs3 = pywt.wavedec(x, haar, mode='sym', level=3)
# Let's see if I can recover the c(1) = (0, 2)
coeffs2 = pywt.wavedec(x, haar, mode='sym', level=2)
decimated = coeffs[0]
# http://wavelets.pybytes.com/wavelet/db2/
scale_vals, wavelet_vals, x_vals = db.wavefun()
plt.plot(x_vals, scale_vals)
def afb1d(x, h0, h1, mode='zero', dim=-1):
""" 1D analysis filter bank (along one dimension only) of an image
Inputs:
x (tensor): 4D input with the last two dimensions the spatial input
h0 (tensor): 4D input for the lowpass filter. Should have shape (1, 1,
h, 1) or (1, 1, 1, w)
h1 (tensor): 4D input for the highpass filter. Should have shape (1, 1,
h, 1) or (1, 1, 1, w)
mode (str): padding method
dim (int) - dimension of filtering. d=2 is for a vertical filter (called
column filtering but filters across the rows). d=3 is for a
horizontal filter, (called row filtering but filters across the
columns).
Returns:
lohi: lowpass and highpass subbands concatenated along the channel
dimension
"""
C = x.shape[1]
# Convert the dim to positive
d = dim % 4
s = (2, 1) if d == 2 else (1, 2)
N = x.shape[d]
# If h0, h1 are not tensors, make them. If they are, then assume that they
# are in the right order
if not isinstance(h0, torch.Tensor):
h0 = torch.tensor(np.copy(np.array(h0).ravel()[::-1]),
dtype=torch.float, device=x.device)
if not isinstance(h1, torch.Tensor):
h1 = torch.tensor(np.copy(np.array(h1).ravel()[::-1]),
dtype=torch.float, device=x.device)
L = h0.numel()
L2 = L // 2
shape = [1, 1, 1, 1]
shape[d] = L
# If h aren't in the right shape, make them so
if h0.shape != tuple(shape):
h0 = h0.reshape(*shape)
if h1.shape != tuple(shape):
h1 = h1.reshape(*shape)
h = torch.cat([h0, h1] * C, dim=0)
if mode == 'per' or mode == 'periodization':
if x.shape[dim] % 2 == 1:
if d == 2:
x = torch.cat((x, x[:, :, -1:]), dim=2)
else:
x = torch.cat((x, x[:, :, :, -1:]), dim=3)
N += 1
x = roll(x, -L2, dim=d)
pad = (L - 1, 0) if d == 2 else (0, L - 1)
lohi = F.conv2d(x, h, padding=pad, stride=s, groups=C)
N2 = N // 2
if d == 2:
lohi[:, :, :L2] = lohi[:, :, :L2] + lohi[:, :, N2:N2 + L2]
lohi = lohi[:, :, :N2]
else:
lohi[:, :, :, :L2] = lohi[:, :, :, :L2] + lohi[:, :, :, N2:N2 + L2]
lohi = lohi[:, :, :, :N2]
else:
# Calculate the pad size
outsize = pywt.dwt_coeff_len(N, L, mode=mode)
p = 2 * (outsize - 1) - N + L
if mode == 'zero':
# Sadly, pytorch only allows for same padding before and after, if
# we need to do more padding after for odd length signals, have to
# prepad
if p % 2 == 1:
pad = (0, 0, 0, 1) if d == 2 else (0, 1, 0, 0)
x = F.pad(x, pad)
pad = (p // 2, 0) if d == 2 else (0, p // 2)
# Calculate the high and lowpass
lohi = F.conv2d(x, h, padding=pad, stride=s, groups=C)
elif mode == 'symmetric' or mode == 'reflect' or mode == 'periodic':
pad = (0, 0, p // 2, (p + 1) // 2) if d == 2 else (p // 2, (p + 1) // 2, 0, 0)
x = mypad(x, pad=pad, mode=mode)
lohi = F.conv2d(x, h, stride=s, groups=C)
else:
raise ValueError("Unkown pad type: {}".format(mode))
return lohi
def coeff_size_list(shape, nscales, wbasis, mode):
"""Construct a size list from given wavelet coefficients.
Related to 1D, 2D and 3D multidimensional wavelet transforms that utilize
`PyWavelets
<http://www.pybytes.com/pywavelets/>`_.
Parameters
----------
shape : `tuple`
Number of pixels/voxels in the image. Its length must be 1, 2 or 3.
nscales : `int`
Number of scales in the multidimensional wavelet
transform. This parameter is checked against the maximum number of
scales returned by ``pywt.dwt_max_level``. For more information
see the `PyWavelets documentation on the maximum level of scales
<http://www.pybytes.com/pywavelets/ref/\
dwt-discrete-wavelet-transform.html#maximum-decomposition-level\
-dwt-max-level>`_.
wbasis : ``pywt.Wavelet``
Selected wavelet basis. For more information see the
`PyWavelets documentation on wavelet bases
<http://www.pybytes.com/pywavelets/ref/wavelets.html>`_.
mode : `str`
Signal extention mode. Possible extension modes are
'zpd': zero-padding -- signal is extended by adding zero samples
'cpd': constant padding -- border values are replicated
'sym': symmetric padding -- signal extension by mirroring samples
'ppd': periodic padding -- signal is trated as a periodic one
'sp1': smooth padding -- signal is extended according to the
first derivatives calculated on the edges (straight line)
'per': periodization -- like periodic-padding but gives the
smallest possible number of decomposition coefficients.
Returns
-------
size_list : `list`
A list containing the sizes of the wavelet (approximation
and detail) coefficients at different scaling levels:
``size_list[0]`` = size of approximation coefficients at
the coarsest level
``size_list[1]`` = size of the detail coefficients at the
coarsest level
...
``size_list[N]`` = size of the detail coefficients at the
finest level
``size_list[N+1]`` = size of the original image
``N`` = number of scaling levels = nscales
"""
if len(shape) not in (1, 2, 3):
raise ValueError('shape must have length 1, 2 or 3, got {}.'
''.format(len(shape)))
max_level = pywt.dwt_max_level(shape[0], filter_len=wbasis.dec_len)
if nscales > max_level:
raise ValueError('Too many scaling levels, got {}, maximum useful'
' level is {}'
''.format(nscales, max_level))
# dwt_coeff_len calculates the number of coefficients at the next
# scaling level given the input size, the length of the filter and
# the applied mode.
# We use this in the following way (per dimension):
# - length[0] = original data length
# - length[n+1] = dwt_coeff_len(length[n], ...)
# - until n = nscales
size_list = [shape]
for scale in range(nscales):
shp = tuple(pywt.dwt_coeff_len(n, filter_len=wbasis.dec_len, mode=mode)
for n in size_list[scale])
size_list.append(shp)
# Add a duplicate of the last entry for the approximation coefficients
size_list.append(size_list[-1])
# We created the list in reversed order compared to what pywt expects
size_list.reverse()
return size_list
def pywt_coeff_shapes(shape, wavelet, nlevels, mode):
"""Return a list of coefficient shapes in the specified transform.
The wavelet transform specified by ``wavelet``, ``nlevels`` and
``mode`` produces a sequence of approximation and detail
coefficients. This function computes the shape of those
coefficient arrays and returns them as a list.
Parameters
----------
shape : sequence
Shape of an input to the transform.
wavelet : string or `pywt.Wavelet`
Specification of the wavelet to be used in the transform.
If a string is given, it is converted to a `pywt.Wavelet`.
Use `pywt.wavelist` to get a list of available wavelets.
nlevels : positive int
Number of scaling levels to be used in the decomposition. The
maximum number of levels can be calculated with
`pywt.dwt_max_level`.
mode : string, optional
PyWavelets style signal extension mode. See `signal extension modes`_
for available options.
Returns
-------
shapes : list
The shapes of the approximation and detail coefficients at
different scaling levels in the following order:
``[shape_aN, shape_DN, ..., shape_D1]``
Here, ``shape_aN`` is the shape of the N-th level approximation
coefficient array, and ``shape_Di`` is the shape of all
i-th level detail coefficients.
See Also
--------
pywt.dwt_coeff_len : function used to determine coefficient sizes at
each scaling level
Examples
--------
Determine the coefficient shapes for 2 scaling levels in 3 dimensions
with zero-padding. Approximation coefficient shape comes first, then
the level-2 detail coefficient and last the level-1 detail coefficient:
>>> pywt_coeff_shapes(shape=(16, 17, 18), wavelet='db2', nlevels=2,
... mode='zero')
[(6, 6, 6), (6, 6, 6), (9, 10, 10)]
References
----------
.. _signal extension modes:
https://pywavelets.readthedocs.io/en/latest/ref/signal-extension-\
modes.html
"""
shape = tuple(shape)
if any(int(s) != s for s in shape):
raise ValueError('`shape` may only contain integers, got {}'
''.format(shape))
wavelet = pywt_wavelet(wavelet)
nlevels, nlevels_in = int(nlevels), nlevels
if nlevels_in != nlevels:
raise ValueError('`nlevels` must be integer, got {}'
''.format(nlevels_in))
# TODO: adapt for axes
for i, n in enumerate(shape):
max_levels = pywt.dwt_max_level(n, wavelet.dec_len)
if max_levels == 0:
raise ValueError('in axis {}: data size {} too small for '
'transform, results in maximal `nlevels` of 0'
''.format(i, n))
if not 0 < nlevels <= max_levels:
raise ValueError('in axis {}: `nlevels` must satisfy 0 < nlevels '
'<= {}, got {}'
''.format(i, max_levels, nlevels))
mode, mode_in = str(mode).lower(), mode
if mode not in PYWT_SUPPORTED_MODES:
raise ValueError("mode '{}' not understood".format(mode_in))
# Use pywt.dwt_coeff_len to determine the coefficient lengths at each
# scale recursively. Start with the image shape and use the last created
# shape for the next step.
shape_list = [shape]
for _ in range(nlevels):
shape = tuple(
pywt.dwt_coeff_len(n, filter_len=wavelet.dec_len, mode=mode)
for n in shape_list[-1])
shape_list.append(shape)
# Add a duplicate of the last entry for the approximation coefficients
shape_list.append(shape_list[-1])
# We created the list in reversed order, reverse it. Remove also the
# superfluous image shape at the end.
shape_list.reverse()
shape_list.pop()
return shape_list
# Multilevel decomposition using
from pywt import wavedec
cA2, cD2, cD1 = wavedec([1, 2, 3, 4, 3, 2, 1], "db1", level=2)
print(cA2)
print(cD2)
print(cD1)
print()
# Partial Discrete Wavelet Transform data decomposition
# Similar to pywt.dwt, but computes only one set of coefficients.
# Useful when you need only approximation or only details at the given level.
coeffs = pywt.downcoef(part="a",
data=[1, 2, 3, 4, 3, 2, 1],
wavelet="db1",
level=2)
print(coeffs)
print()
# Maximum decomposition level
w = pywt.Wavelet("sym5")
l = pywt.dwt_max_level(data_len=1000, filter_len=w.dec_len)
print(l)
l = pywt.dwt_max_level(data_len=1000, filter_len=w)
print(l)
print()
# Result coefficients length
l = pywt.dwt_coeff_len(data_len=1000, filter_len=w, mode="per")
print(l)
def discrete_wavelet_transform_example():
x = [3, 7, 1, 1, -2, 5, 4, 6]
cA, cD = pywt.dwt(x, 'db2') # Approximation and detail coefficients.
print('Approximation coefficients =', cA)
print('Detail coefficients =', cD)
print('Single level reconstruction of signal =', pywt.idwt(cA, cD, 'db2'))
#--------------------
# Pass a Wavelet object instead of the wavelet name and specify signal extension mode (the default is symmetric) for the border effect handling
w = pywt.Wavelet('sym3')
# the output coefficients arrays length depends not only on the input data length but also on the :class:Wavelet type (particularly on its filters length that are used in the transformation).
# If you expected that the output length would be a half of the input data length, well, that's the trade-off that allows for the perfect reconstruction…
cA, cD = pywt.dwt(x, wavelet=w, mode='constant')
print('Approximation coefficients =', cA)
print('Detail coefficients =', cD)
# To find out what will be the output data size use the dwt_coeff_len() function.
print(
'Length of coefficients =',
int(
pywt.dwt_coeff_len(data_len=len(x),
filter_len=w.dec_len,
mode='symmetric')))
print('Length of coefficients =',
int(pywt.dwt_coeff_len(len(x), w, 'symmetric')))
print('Length of coefficients =', len(cA))
# The periodization (periodization) mode is slightly different from the others.
# It's aim when doing the DWT transform is to output coefficients arrays that are half of the length of the input data.
# Knowing that, you should never mix the periodization mode with other modes when doing DWT and IDWT.
# Otherwise, it will produce invalid results.
cA, cD = pywt.dwt(x, wavelet=w, mode='periodization')
print('Single level reconstruction of signal =',
pywt.idwt(cA, cD, 'sym3', 'symmetric')) # Invalid mode.
print('Single level reconstruction of signal =',
pywt.idwt(cA, cD, 'sym3', 'periodization'))
# Passing None as one of the coefficient arrays parameters is similar to passing a zero-filled array.
print('Single level reconstruction of signal =',
pywt.idwt([1, 2, 0, 1], None, 'db2', 'symmetric'))
print('Single level reconstruction of signal =',
pywt.idwt([1, 2, 0, 1], [0, 0, 0, 0], 'db2', 'symmetric'))
print('Single level reconstruction of signal =',
pywt.idwt(None, [1, 2, 0, 1], 'db2', 'symmetric'))
print('Single level reconstruction of signal =',
pywt.idwt([0, 0, 0, 0], [1, 2, 0, 1], 'db2', 'symmetric'))
# Only one argument at a time can be None.
try:
print('Single level reconstruction of signal =',
pywt.idwt(None, None, 'db2', 'symmetric'))
except ValueError as ex:
print('Invalid coefficient parameter.')
# When doing the IDWT transform, usually the coefficient arrays must have the same size.
try:
pywt.idwt([1, 2, 3, 4, 5], [1, 2, 3, 4], 'db2', 'symmetric')
except ValueError as ex:
print('Invalid size of coefficients arrays.')
# Not every coefficient array can be used in IDWT.
try:
pywt.idwt([1, 2, 4], [4, 1, 3], 'db4', 'symmetric')
except ValueError as ex:
print('Invalid coefficient arrays length.')
print('Coefficient length =',
int(pywt.dwt_coeff_len(1,
pywt.Wavelet('db4').dec_len, 'symmetric')))
>>> w = pywt.Wavelet('sym3')
>>> cA, cD = pywt.dwt(x, wavelet=w, mode='cpd')
>>> print cA
[ 4.38354585 3.80302657 7.31813271 -0.58565539 4.09727044 7.81994027]
>>> print cD
[-1.33068221 -2.78795192 -3.16825651 -0.67715519 -0.09722957 -0.07045258]
注意这里输出的系数数组长度不只跟输入数据的长度有关，还和Wavelet类型有关（特别是它所使用的滤波器长度）。
如果想查看输出数据的长度可以使用dwt_coeff_len()函数：
>>> pywt.dwt_coeff_len(data_len=len(x), filter_len=w.dec_len, mode='sym')
6
>>> pywt.dwt_coeff_len(len(x), w, 'sym')
6
>>> len(cA)
6
dwt_coeff_len（）函数的第三个参数是mode。
>>> pywt.MODES.modes
['zpd', 'cpd', 'sym', 'ppd', 'sp1', 'per']
>>> [pywt.dwt_coeff_len(len(x), w.dec_len, mode) for mode in pywt.MODES.modes]
[6, 6, 6, 6, 6, 4]
def pywt_coeff_shapes(shape, wavelet, nlevels, mode):
"""Return a list of coefficient shapes in the specified transform.
The wavelet transform specified by ``wavelet``, ``nlevels`` and
``mode`` produces a sequence of approximation and detail
coefficients. This function computes the shape of those
coefficient arrays and returns them as a list.
Parameters
----------
shape : sequence
Shape of an input to the transform.
wavelet : string or `pywt.Wavelet`
Specification of the wavelet to be used in the transform.
If a string is given, it is converted to a `pywt.Wavelet`.
Use `pywt.wavelist` to get a list of available wavelets.
nlevels : positive int
Number of scaling levels to be used in the decomposition. The
maximum number of levels can be calculated with
`pywt.dwt_max_level`.
mode : string, optional
PyWavelets style signal extension mode. See `signal extension modes`_
for available options.
Returns
-------
shapes : list
The shapes of the approximation and detail coefficients at
different scaling levels in the following order:
``[shape_aN, shape_DN, ..., shape_D1]``
Here, ``shape_aN`` is the shape of the N-th level approximation
coefficient array, and ``shape_Di`` is the shape of all
i-th level detail coefficients.
See Also
--------
pywt.dwt_coeff_len : function used to determine coefficient sizes at
each scaling level
Examples
--------
Determine the coefficient shapes for 2 scaling levels in 3 dimensions
with zero-padding. Approximation coefficient shape comes first, then
the level-2 detail coefficient and last the level-1 detail coefficient:
>>> pywt_coeff_shapes(shape=(16, 17, 18), wavelet='db2', nlevels=2,
... mode='zero')
[(6, 6, 6), (6, 6, 6), (9, 10, 10)]
References
----------
.. _signal extension modes:
https://pywavelets.readthedocs.io/en/latest/ref/signal-extension-\
modes.html
"""
shape = tuple(shape)
if any(int(s) != s for s in shape):
raise ValueError('`shape` may only contain integers, got {}'
''.format(shape))
wavelet = pywt_wavelet(wavelet)
nlevels, nlevels_in = int(nlevels), nlevels
if nlevels_in != nlevels:
raise ValueError('`nlevels` must be integer, got {}'
''.format(nlevels_in))
# TODO: adapt for axes
for i, n in enumerate(shape):
max_levels = pywt.dwt_max_level(n, wavelet.dec_len)
if max_levels == 0:
raise ValueError('in axis {}: data size {} too small for '
'transform, results in maximal `nlevels` of 0'
''.format(i, n))
if not 0 < nlevels <= max_levels:
raise ValueError('in axis {}: `nlevels` must satisfy 0 < nlevels '
'<= {}, got {}'
''.format(i, max_levels, nlevels))
mode, mode_in = str(mode).lower(), mode
if mode not in PYWT_SUPPORTED_MODES:
raise ValueError("mode '{}' not understood".format(mode_in))
# Use pywt.dwt_coeff_len to determine the coefficient lengths at each
# scale recursively. Start with the image shape and use the last created
# shape for the next step.
shape_list = [shape]
for _ in range(nlevels):
shape = tuple(pywt.dwt_coeff_len(n, filter_len=wavelet.dec_len,
mode=mode)
for n in shape_list[-1])
shape_list.append(shape)
# Add a duplicate of the last entry for the approximation coefficients
shape_list.append(shape_list[-1])
# We created the list in reversed order, reverse it. Remove also the
# superfluous image shape at the end.
shape_list.reverse()
shape_list.pop()
return shape_list
def coeff_len(self, input_length):
return pywt.dwt_coeff_len(input_length, self.dec_lo.shape[0],
self.mode)
