def __init__(self,
biort='farras',
qshift='qshift_a',
J=3,
mode='symmetric'):
super().__init__()
self.biort = biort
self.qshift = qshift
self.J = J
if isinstance(biort, str):
biort = _level1(biort)
assert len(biort) == 8
h0a1, h0b1, _, _, h1a1, h1b1, _, _ = biort
DWTaa1 = DWTForward(J=1, wave=(h0a1, h1a1, h0a1, h1a1), mode=mode)
DWTab1 = DWTForward(J=1, wave=(h0a1, h1a1, h0b1, h1b1), mode=mode)
DWTba1 = DWTForward(J=1, wave=(h0b1, h1b1, h0a1, h1a1), mode=mode)
DWTbb1 = DWTForward(J=1, wave=(h0b1, h1b1, h0b1, h1b1), mode=mode)
self.level1 = nn.ModuleList([DWTaa1, DWTab1, DWTba1, DWTbb1])
if J > 1:
if isinstance(qshift, str):
qshift = _qshift(qshift)
assert len(qshift) == 8
h0a, h0b, _, _, h1a, h1b, _, _ = qshift
DWTaa = DWTForward(J - 1, (h0a, h1a, h0a, h1a), mode=mode)
DWTab = DWTForward(J - 1, (h0a, h1a, h0b, h1b), mode=mode)
DWTba = DWTForward(J - 1, (h0b, h1b, h0a, h1a), mode=mode)
DWTbb = DWTForward(J - 1, (h0b, h1b, h0b, h1b), mode=mode)
self.level2 = nn.ModuleList([DWTaa, DWTab, DWTba, DWTbb])
def icplxdual2D(yl, yh, level1='farras', qshift='qshift_a', mode='periodization'):
# Get the filters
_, _, g0a1, g0b1, _, _, g1a1, g1b1 = _level1(level1)
_, _, g0a, g0b, _, _, g1a, g1b = _qshift(qshift)
dev = yl[0][0].device
Faf = ((prep_filt_sfb2d(g0a1, g1a1, g0a1, g1a1, device=dev),
prep_filt_sfb2d(g0a1, g1a1, g0b1, g1b1, device=dev)),
(prep_filt_sfb2d(g0b1, g1b1, g0a1, g1a1, device=dev),
prep_filt_sfb2d(g0b1, g1b1, g0b1, g1b1, device=dev)))
af = ((prep_filt_sfb2d(g0a, g1a, g0a, g1a, device=dev),
prep_filt_sfb2d(g0a, g1a, g0b, g1b, device=dev)),
(prep_filt_sfb2d(g0b, g1b, g0a, g1a, device=dev),
prep_filt_sfb2d(g0b, g1b, g0b, g1b, device=dev)))
# Convert the highs back to subbands
J = len(yh)
w = [[[[None for i in range(3)] for j in range(2)] for k in range(2)] for l in range(J)]
for j in range(J):
w[j][0][0][0], w[j][1][1][0] = pm(yh[j][:,2,:,:,:,0],
yh[j][:,3,:,:,:,1])
w[j][0][1][0], w[j][1][0][0] = pm(yh[j][:,3,:,:,:,0],
yh[j][:,2,:,:,:,1])
w[j][0][0][1], w[j][1][1][1] = pm(yh[j][:,0,:,:,:,0],
yh[j][:,5,:,:,:,1])
w[j][0][1][1], w[j][1][0][1] = pm(yh[j][:,5,:,:,:,0],
yh[j][:,0,:,:,:,1])
w[j][0][0][2], w[j][1][1][2] = pm(yh[j][:,1,:,:,:,0],
yh[j][:,4,:,:,:,1])
w[j][0][1][2], w[j][1][0][2] = pm(yh[j][:,4,:,:,:,0],
yh[j][:,1,:,:,:,1])
w[j][0][0] = torch.stack(w[j][0][0], dim=2)
w[j][0][1] = torch.stack(w[j][0][1], dim=2)
w[j][1][0] = torch.stack(w[j][1][0], dim=2)
w[j][1][1] = torch.stack(w[j][1][1], dim=2)
y = None
for m in range(2):
for n in range(2):
lo = yl[m][n]
for j in range(J-1, 0, -1):
lo = sfb2d(lo, w[j][m][n], af[m][n], mode=mode)
lo = sfb2d(lo, w[0][m][n], Faf[m][n], mode=mode)
# Add to the output
if y is None:
y = lo
else:
y = y + lo
# Normalize
y = y/2
return y
def __init__(self, biort='farras', qshift='qshift_a', mode='symmetric'):
super().__init__()
self.biort = biort
self.qshift = qshift
if isinstance(biort, str):
biort = _level1(biort)
assert len(biort) == 8
_, _, g0a1, g0b1, _, _, g1a1, g1b1 = biort
IWTaa1 = DWTInverse(wave=(g0a1, g1a1, g0a1, g1a1), mode=mode)
IWTab1 = DWTInverse(wave=(g0a1, g1a1, g0b1, g1b1), mode=mode)
IWTba1 = DWTInverse(wave=(g0b1, g1b1, g0a1, g1a1), mode=mode)
IWTbb1 = DWTInverse(wave=(g0b1, g1b1, g0b1, g1b1), mode=mode)
self.level1 = nn.ModuleList([IWTaa1, IWTab1, IWTba1, IWTbb1])
if isinstance(qshift, str):
qshift = _qshift(qshift)
assert len(qshift) == 8
_, _, g0a, g0b, _, _, g1a, g1b = qshift
IWTaa = DWTInverse(wave=(g0a, g1a, g0a, g1a), mode=mode)
IWTab = DWTInverse(wave=(g0a, g1a, g0b, g1b), mode=mode)
IWTba = DWTInverse(wave=(g0b, g1b, g0a, g1a), mode=mode)
IWTbb = DWTInverse(wave=(g0b, g1b, g0b, g1b), mode=mode)
self.level2 = nn.ModuleList([IWTaa, IWTab, IWTba, IWTbb])
def cplxdual2D(x,
J,
level1='farras',
qshift='qshift_a',
mode='periodization',
mag=False):
""" Do a complex dtcwt
Returns:
lows: lowpass outputs from each of the 4 trees. Is a 2x2 list of lists
w: bandpass outputs from each of the 4 trees. Is a list of lists, with
shape [J][2][2][3]. Initially the 3 outputs are the lh, hl and hh from
each of the 4 trees. After doing sums and differences though, they
become the real and imaginary parts for the 6 orientations. In
particular:
first index - indexes over scales
second index - 0 = real, 1 = imaginary
third and fourth indices:
0,1 = 15 degrees
1,2 = 45 degrees
0,0 = 75 degrees
1,0 = 105 degrees
0,2 = 135 degrees
1,1 = 165 degrees
"""
x = x / 2
# Get the filters
h0a1, h0b1, _, _, h1a1, h1b1, _, _ = _level1(level1)
h0a, h0b, _, _, h1a, h1b, _, _ = _qshift(qshift)
Faf = ((prep_filt_afb2d(h0a1, h1a1, h0a1, h1a1, device=x.device),
prep_filt_afb2d(h0a1, h1a1, h0b1, h1b1, device=x.device)),
(prep_filt_afb2d(h0b1, h1b1, h0a1, h1a1, device=x.device),
prep_filt_afb2d(h0b1, h1b1, h0b1, h1b1, device=x.device)))
af = ((prep_filt_afb2d(h0a, h1a, h0a, h1a, device=x.device),
prep_filt_afb2d(h0a, h1a, h0b, h1b, device=x.device)),
(prep_filt_afb2d(h0b, h1b, h0a, h1a, device=x.device),
prep_filt_afb2d(h0b, h1b, h0b, h1b, device=x.device)))
# Do 4 fully decimated dwts
w = [[[None for _ in range(2)] for _ in range(2)] for j in range(J)]
lows = [[None for _ in range(2)] for _ in range(2)]
for m in range(2):
for n in range(2):
# Do the first level transform with the first level filters
# ll, bands = afb2d(x, (Faf[m][0], Faf[m][1], Faf[n][0], Faf[n][1]), mode=mode)
bands = afb2d(x, Faf[m][n], mode=mode)
# Separate the low and bandpasses
s = bands.shape
bands = bands.reshape(s[0], -1, 4, s[-2], s[-1])
ll = bands[:, :, 0].contiguous()
w[0][m][n] = [bands[:, :, 2], bands[:, :, 1], bands[:, :, 3]]
# Do the second+ level transform with the second level filters
for j in range(1, J):
# ll, bands = afb2d(ll, (af[m][0], af[m][1], af[n][0], af[n][1]), mode=mode)
bands = afb2d(ll, af[m][n], mode=mode)
# Separate the low and bandpasses
s = bands.shape
bands = bands.reshape(s[0], -1, 4, s[-2], s[-1])
ll = bands[:, :, 0].contiguous()
w[j][m][n] = [bands[:, :, 2], bands[:, :, 1], bands[:, :, 3]]
lows[m][n] = ll
# Convert the quads into real and imaginary parts
yh = [
None,
] * J
for j in range(J):
deg75r, deg105i = pm(w[j][0][0][0], w[j][1][1][0])
deg105r, deg75i = pm(w[j][0][1][0], w[j][1][0][0])
deg15r, deg165i = pm(w[j][0][0][1], w[j][1][1][1])
deg165r, deg15i = pm(w[j][0][1][1], w[j][1][0][1])
deg135r, deg45i = pm(w[j][0][0][2], w[j][1][1][2])
deg45r, deg135i = pm(w[j][0][1][2], w[j][1][0][2])
yhr = torch.stack((deg15r, deg45r, deg75r, deg105r, deg135r, deg165r),
dim=1)
yhi = torch.stack((deg15i, deg45i, deg75i, deg105i, deg135i, deg165i),
dim=1)
if mag:
yh[j] = torch.sqrt(yhr**2 + yhi**2 + 0.01) - np.sqrt(0.01)
else:
yh[j] = torch.stack((yhr, yhi), dim=-1)
return lows, yh