def test_odd_filter():
colifilt(lena, (-1,2,-1), (-1,2,1))
def test_different_size_h():
colifilt(lena, (-1,2,1), (-0.5,-1,2,-1,0.5))
def _level2_ifm(Yl, Yh, g0a, g0b, g1a, g1b, ext_mode, prev_level_size):
"""Perform level 2 or greater of the 3d inverse transform.
"""
# Create work area
work = np.zeros(np.asanyarray(Yl.shape)*2, dtype=Yl.dtype)
# Form some useful slices
s0a = slice(None, work.shape[0] >> 1)
s1a = slice(None, work.shape[1] >> 1)
s2a = slice(None, work.shape[2] >> 1)
s0b = slice(work.shape[0] >> 1, None)
s1b = slice(work.shape[1] >> 1, None)
s2b = slice(work.shape[2] >> 1, None)
# Assign regions of work area
work[s0a, s1a, s2a] = Yl
work[s0a, s1b, s2a] = c2cube(Yh[:,:,:, 0:4 ])
work[s0b, s1a, s2a] = c2cube(Yh[:,:,:, 4:8 ])
work[s0b, s1b, s2a] = c2cube(Yh[:,:,:, 8:12])
work[s0a, s1a, s2b] = c2cube(Yh[:,:,:,12:16])
work[s0a, s1b, s2b] = c2cube(Yh[:,:,:,16:20])
work[s0b, s1a, s2b] = c2cube(Yh[:,:,:,20:24])
work[s0b, s1b, s2b] = c2cube(Yh[:,:,:,24:28])
for f in xrange(work.shape[2]):
# Do even Qshift filters on rows.
y = colifilt(work[:, s1a, f].T, g0b, g0a) + colifilt(work[:, s1b, f].T, g1b, g1a)
# Do even Qshift filters on columns.
work[:, :, f] = colifilt(y[:, s0a].T, g0b, g0a) + colifilt(y[:,s0b].T, g1b, g1a)
for f in xrange(work.shape[1]):
# Do even Qshift filters on 3rd dim.
y = work[:, f, :].T
work[:, f, :] = (colifilt(y[s2a, :], g0b, g0a) + colifilt(y[s2b, :], g1b, g1a)).T
# Now check if the size of the previous level is exactly twice the size of
# the current level. If YES, this means we have not done the extension in
# the previous level. If NO, then we have to remove the appended row /
# column / frame from the previous level DTCWT coefs.
prev_level_size = np.asarray(prev_level_size)
curr_level_size = np.asarray(Yh.shape)
if ext_mode == 4:
if curr_level_size[0] * 2 != prev_level_size[0]:
# Discard the top and bottom rows
work = work[1:-1,:,:]
if curr_level_size[1] * 2 != prev_level_size[1]:
# Discard the top and bottom rows
work = work[:,1:-1,:]
if curr_level_size[2] * 2 != prev_level_size[2]:
# Discard the top and bottom rows
work = work[:,:,1:-1]
elif ext_mode == 8:
if curr_level_size[0] * 2 != prev_level_size[0]:
# Discard the top and bottom rows
work = work[2:-2,:,:]
if curr_level_size[1] * 2 != prev_level_size[1]:
# Discard the top and bottom rows
work = work[:,2:-2,:]
if curr_level_size[2] * 2 != prev_level_size[2]:
# Discard the top and bottom rows
work = work[:,:,2:-2]
return work
def dtwaveifm(Yl,
Yh,
biort=DEFAULT_BIORT,
qshift=DEFAULT_QSHIFT,
gain_mask=None):
"""Perform an *n*-level dual-tree complex wavelet (DTCWT) 1D
reconstruction.
:param Yl: The real lowpass subband from the final level
:param Yh: A sequence containing the complex highpass subband for each level.
:param biort: Level 1 wavelets to use. See :py:func:`biort`.
:param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.
:param gain_mask: Gain to be applied to each subband.
:returns Z: Reconstructed real array.
The *l*-th element of *gain_mask* is gain for wavelet subband at level l.
If gain_mask[l] == 0, no computation is performed for band *l*. Default
*gain_mask* is all ones. Note that *l* is 0-indexed.
If *biort* or *qshift* are strings, they are used as an argument to the
:py:func:`biort` or :py:func:`qshift` functions. Otherwise, they are
interpreted as tuples of vectors giving filter coefficients. In the *biort*
case, this should be (h0o, g0o, h1o, g1o). In the *qshift* case, this should
be (h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b).
Example::
# Performs a reconstruction from Yl,Yh using the 13,19-tap filters
# for level 1 and the Q-shift 14-tap filters for levels >= 2.
Z = dtwaveifm(Yl, Yh, 'near_sym_b', 'qshift_b')
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, May 2002
.. codeauthor:: Cian Shaffrey, Cambridge University, May 2002
"""
a = len(Yh) # No of levels.
if gain_mask is None:
gain_mask = np.ones(a) # Default gain_mask.
# Try to load coefficients if biort is a string parameter
try:
h0o, g0o, h1o, g1o = _biort(biort)
except TypeError:
h0o, g0o, h1o, g1o = biort
# Try to load coefficients if qshift is a string parameter
try:
h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = _qshift(qshift)
except TypeError:
h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = qshift
level = a - 1 # No of levels = no of rows in L.
if level < 0:
# if there are no levels in the input, just return the Yl value
return Yl
Lo = Yl
while level >= 1: # Reconstruct levels 2 and above in reverse order.
Hi = c2q1d(Yh[level] * gain_mask[level])
Lo = colifilt(Lo, g0b, g0a) + colifilt(Hi, g1b, g1a)
if Lo.shape[0] != 2 * Yh[level - 1].shape[
0]: # If Lo is not the same length as the next Yh => t1 was extended.
Lo = Lo[
1:-1,
...] # Therefore we have to clip Lo so it is the same height as the next Yh.
if np.any(
np.asanyarray(Lo.shape) != np.asanyarray(Yh[level - 1].shape *
np.array((2, 1)))):
raise ValueError('Yh sizes are not valid for DTWAVEIFM')
level -= 1
if level == 0: # Reconstruct level 1.
Hi = c2q1d(Yh[level] * gain_mask[level])
Z = colfilter(Lo, g0o) + colfilter(Hi, g1o)
# Return a 1d vector or a column vector
if Z.shape[1] == 1:
return Z.flatten()
else:
return Z
def test_output_size_non_mult_4():
Y = colifilt(lena, (-1,0,0,1), (1,0,0,-1))
assert Y.shape == (lena.shape[0]*2, lena.shape[1])
def dtwaveifm2(Yl,Yh,biort=DEFAULT_BIORT,qshift=DEFAULT_QSHIFT,gain_mask=None):
"""Perform an *n*-level dual-tree complex wavelet (DTCWT) 2D
reconstruction.
:param Yl: The real lowpass subband from the final level
:param Yh: A sequence containing the complex highpass subband for each level.
:param biort: Level 1 wavelets to use. See :py:func:`biort`.
:param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.
:param gain_mask: Gain to be applied to each subband.
:returns Z: Reconstructed real array
The (*d*, *l*)-th element of *gain_mask* is gain for subband with direction
*d* at level *l*. If gain_mask[d,l] == 0, no computation is performed for
band (d,l). Default *gain_mask* is all ones. Note that both *d* and *l* are
zero-indexed.
If *biort* or *qshift* are strings, they are used as an argument to the
:py:func:`biort` or :py:func:`qshift` functions. Otherwise, they are
interpreted as tuples of vectors giving filter coefficients. In the *biort*
case, this should be (h0o, g0o, h1o, g1o). In the *qshift* case, this should
be (h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b).
Example::
# Performs a 3-level reconstruction from Yl,Yh using the 13,19-tap
# filters for level 1 and the Q-shift 14-tap filters for levels >= 2.
Z = dtwaveifm2(Yl, Yh, 'near_sym_b', 'qshift_b')
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, May 2002
.. codeauthor:: Cian Shaffrey, Cambridge University, May 2002
"""
a = len(Yh) # No of levels.
if gain_mask is None:
gain_mask = np.ones((6,a)) # Default gain_mask.
gain_mask = np.array(gain_mask)
# Try to load coefficients if biort is a string parameter
try:
h0o, g0o, h1o, g1o = _biort(biort)
except TypeError:
h0o, g0o, h1o, g1o = biort
# Try to load coefficients if qshift is a string parameter
try:
h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = _qshift(qshift)
except TypeError:
h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = qshift
current_level = a
Z = Yl
while current_level >= 2: # this ensures that for level 1 we never do the following
lh = c2q(Yh[current_level-1][:,:,[0, 5]], gain_mask[[0, 5], current_level-1])
hl = c2q(Yh[current_level-1][:,:,[2, 3]], gain_mask[[2, 3], current_level-1])
hh = c2q(Yh[current_level-1][:,:,[1, 4]], gain_mask[[1, 4], current_level-1])
# Do even Qshift filters on columns.
y1 = colifilt(Z,g0b,g0a) + colifilt(lh,g1b,g1a)
y2 = colifilt(hl,g0b,g0a) + colifilt(hh,g1b,g1a)
# Do even Qshift filters on rows.
Z = (colifilt(y1.T,g0b,g0a) + colifilt(y2.T,g1b,g1a)).T
# Check size of Z and crop as required
[row_size, col_size] = Z.shape
S = 2*np.array(Yh[current_level-2].shape)
if row_size != S[0]: # check to see if this result needs to be cropped for the rows
Z = Z[1:-1,:]
if col_size != S[1]: # check to see if this result needs to be cropped for the cols
Z = Z[:,1:-1]
if np.any(np.array(Z.shape) != S[:2]):
raise ValueError('Sizes of subbands are not valid for DTWAVEIFM2')
current_level = current_level - 1
if current_level == 1:
lh = c2q(Yh[current_level-1][:,:,[0, 5]],gain_mask[[0, 5],current_level-1])
hl = c2q(Yh[current_level-1][:,:,[2, 3]],gain_mask[[2, 3],current_level-1])
hh = c2q(Yh[current_level-1][:,:,[1, 4]],gain_mask[[1, 4],current_level-1])
# Do odd top-level filters on columns.
y1 = colfilter(Z,g0o) + colfilter(lh,g1o)
y2 = colfilter(hl,g0o) + colfilter(hh,g1o)
# Do odd top-level filters on rows.
Z = (colfilter(y1.T,g0o) + colfilter(y2.T,g1o)).T
return Z
def test_output_size():
Y = colifilt(lena, (-1, 1), (1, -1))
assert Y.shape == (lena.shape[0] * 2, lena.shape[1])
def test_good_input_size():
colifilt(lena[:,:511], (-1,1), (1,-1))
def test_bad_input_size():
colifilt(lena[:511, :], (-1, 1), (1, -1))
def test_good_input_size():
colifilt(lena[:, :511], (-1, 1), (1, -1))
def test_zero_input():
Y = colifilt(np.zeros_like(lena), (-1, 1), (1, -1))
assert np.all(Y[:0] == 0)
def test_different_size_h():
colifilt(lena, (-1, 2, 1), (-0.5, -1, 2, -1, 0.5))
def test_odd_filter():
colifilt(lena, (-1, 2, -1), (-1, 2, 1))
def test_zero_input():
Y = colifilt(np.zeros_like(lena), (-1,1), (1,-1))
assert np.all(Y[:0] == 0)
def test_output_size_non_mult_4():
Y = colifilt(lena, (-1, 0, 0, 1), (1, 0, 0, -1))
assert Y.shape == (lena.shape[0] * 2, lena.shape[1])
def test_bad_input_size():
colifilt(lena[:511,:], (-1,1), (1,-1))
def test_non_orthogonal_input_non_mult_4():
Y = colifilt(lena, (1, 0, 0, 1), (1, 0, 0, 1))
assert Y.shape == (lena.shape[0] * 2, lena.shape[1])
def test_output_size():
Y = colifilt(lena, (-1,1), (1,-1))
assert Y.shape == (lena.shape[0]*2, lena.shape[1])
def dtwaveifm(Yl, Yh, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, gain_mask=None):
"""Perform an *n*-level dual-tree complex wavelet (DTCWT) 1D
reconstruction.
:param Yl: The real lowpass subband from the final level
:param Yh: A sequence containing the complex highpass subband for each level.
:param biort: Level 1 wavelets to use. See :py:func:`biort`.
:param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.
:param gain_mask: Gain to be applied to each subband.
:returns Z: Reconstructed real array.
The *l*-th element of *gain_mask* is gain for wavelet subband at level l.
If gain_mask[l] == 0, no computation is performed for band *l*. Default
*gain_mask* is all ones. Note that *l* is 0-indexed.
If *biort* or *qshift* are strings, they are used as an argument to the
:py:func:`biort` or :py:func:`qshift` functions. Otherwise, they are
interpreted as tuples of vectors giving filter coefficients. In the *biort*
case, this should be (h0o, g0o, h1o, g1o). In the *qshift* case, this should
be (h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b).
Example::
# Performs a reconstruction from Yl,Yh using the 13,19-tap filters
# for level 1 and the Q-shift 14-tap filters for levels >= 2.
Z = dtwaveifm(Yl, Yh, 'near_sym_b', 'qshift_b')
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, May 2002
.. codeauthor:: Cian Shaffrey, Cambridge University, May 2002
"""
a = len(Yh) # No of levels.
if gain_mask is None:
gain_mask = np.ones(a) # Default gain_mask.
# Try to load coefficients if biort is a string parameter
try:
h0o, g0o, h1o, g1o = _biort(biort)
except TypeError:
h0o, g0o, h1o, g1o = biort
# Try to load coefficients if qshift is a string parameter
try:
h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = _qshift(qshift)
except TypeError:
h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = qshift
level = a-1 # No of levels = no of rows in L.
if level < 0:
# if there are no levels in the input, just return the Yl value
return Yl
Lo = Yl
while level >= 1: # Reconstruct levels 2 and above in reverse order.
Hi = c2q1d(Yh[level]*gain_mask[level])
Lo = colifilt(Lo, g0b, g0a) + colifilt(Hi, g1b, g1a)
if Lo.shape[0] != 2*Yh[level-1].shape[0]: # If Lo is not the same length as the next Yh => t1 was extended.
Lo = Lo[1:-1,...] # Therefore we have to clip Lo so it is the same height as the next Yh.
if np.any(np.asanyarray(Lo.shape) != np.asanyarray(Yh[level-1].shape * np.array((2,1)))):
raise ValueError('Yh sizes are not valid for DTWAVEIFM')
level -= 1
if level == 0: # Reconstruct level 1.
Hi = c2q1d(Yh[level]*gain_mask[level])
Z = colfilter(Lo,g0o) + colfilter(Hi,g1o)
# Return a 1d vector or a column vector
if Z.shape[1] == 1:
return Z.flatten()
else:
return Z
def test_non_orthogonal_input_non_mult_4():
Y = colifilt(lena, (1,0,0,1), (1,0,0,1))
assert Y.shape == (lena.shape[0]*2, lena.shape[1])
def dtwaveifm2(Yl, Yh, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, gain_mask=None):
"""Perform an *n*-level dual-tree complex wavelet (DTCWT) 2D
reconstruction.
:param Yl: The real lowpass subband from the final level
:param Yh: A sequence containing the complex highpass subband for each level.
:param biort: Level 1 wavelets to use. See :py:func:`biort`.
:param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.
:param gain_mask: Gain to be applied to each subband.
:returns Z: Reconstructed real array
The (*d*, *l*)-th element of *gain_mask* is gain for subband with direction
*d* at level *l*. If gain_mask[d,l] == 0, no computation is performed for
band (d,l). Default *gain_mask* is all ones. Note that both *d* and *l* are
zero-indexed.
If *biort* or *qshift* are strings, they are used as an argument to the
:py:func:`biort` or :py:func:`qshift` functions. Otherwise, they are
interpreted as tuples of vectors giving filter coefficients. In the *biort*
case, this should be (h0o, g0o, h1o, g1o). In the *qshift* case, this should
be (h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b).
Example::
# Performs a 3-level reconstruction from Yl,Yh using the 13,19-tap
# filters for level 1 and the Q-shift 14-tap filters for levels >= 2.
Z = dtwaveifm2(Yl, Yh, 'near_sym_b', 'qshift_b')
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, May 2002
.. codeauthor:: Cian Shaffrey, Cambridge University, May 2002
"""
a = len(Yh) # No of levels.
if gain_mask is None:
gain_mask = np.ones((6, a)) # Default gain_mask.
gain_mask = np.array(gain_mask)
# Try to load coefficients if biort is a string parameter
try:
h0o, g0o, h1o, g1o = _biort(biort)
except TypeError:
h0o, g0o, h1o, g1o = biort
# Try to load coefficients if qshift is a string parameter
try:
h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = _qshift(qshift)
except TypeError:
h0a, h0b, g0a, g0b, h1a, h1b, g1a, g1b = qshift
current_level = a
Z = Yl
while current_level >= 2: # this ensures that for level 1 we never do the following
lh = c2q(Yh[current_level - 1][:, :, [0, 5]], gain_mask[[0, 5], current_level - 1])
hl = c2q(Yh[current_level - 1][:, :, [2, 3]], gain_mask[[2, 3], current_level - 1])
hh = c2q(Yh[current_level - 1][:, :, [1, 4]], gain_mask[[1, 4], current_level - 1])
# Do even Qshift filters on columns.
y1 = colifilt(Z, g0b, g0a) + colifilt(lh, g1b, g1a)
y2 = colifilt(hl, g0b, g0a) + colifilt(hh, g1b, g1a)
# Do even Qshift filters on rows.
Z = (colifilt(y1.T, g0b, g0a) + colifilt(y2.T, g1b, g1a)).T
# Check size of Z and crop as required
[row_size, col_size] = Z.shape
S = 2 * np.array(Yh[current_level - 2].shape)
if row_size != S[0]: # check to see if this result needs to be cropped for the rows
Z = Z[1:-1, :]
if col_size != S[1]: # check to see if this result needs to be cropped for the cols
Z = Z[:, 1:-1]
if np.any(np.array(Z.shape) != S[:2]):
raise ValueError("Sizes of subbands are not valid for DTWAVEIFM2")
current_level = current_level - 1
if current_level == 1:
lh = c2q(Yh[current_level - 1][:, :, [0, 5]], gain_mask[[0, 5], current_level - 1])
hl = c2q(Yh[current_level - 1][:, :, [2, 3]], gain_mask[[2, 3], current_level - 1])
hh = c2q(Yh[current_level - 1][:, :, [1, 4]], gain_mask[[1, 4], current_level - 1])
# Do odd top-level filters on columns.
y1 = colfilter(Z, g0o) + colfilter(lh, g1o)
y2 = colfilter(hl, g0o) + colfilter(hh, g1o)
# Do odd top-level filters on rows.
Z = (colfilter(y1.T, g0o) + colfilter(y2.T, g1o)).T
return Z
