def __init__(self, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT):
try:
self.biort = _biort(biort)
except TypeError:
self.biort = biort
# Load quarter sample shift wavelets
try:
self.qshift = _qshift(qshift)
except TypeError:
self.qshift = qshift
def __init__(self, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT):
# Load bi-orthogonal wavelets
try:
self.biort = _biort(biort)
except TypeError:
self.biort = biort
# Load quarter sample shift wavelets
try:
self.qshift = _qshift(qshift)
except TypeError:
self.qshift = qshift
def __init__(self, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, ext_mode=4):
# Load bi-orthogonal wavelets
try:
self.biort = _biort(biort)
except TypeError:
self.biort = biort
# Load quarter sample shift wavelets
try:
self.qshift = _qshift(qshift)
except TypeError:
self.qshift = qshift
self.ext_mode = ext_mode
def __init__(self, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, ext_mode=4, discard_level_1=False):
"""
Constructor for the 3D DT-CWT transform class (NumPy).
:param biort: Level 1 wavelets to use. See :py:func:`dtcwt.coeffs.biort`.
:param qshift: Level >= 2 wavelets to use. See :py:func:`dtcwt.coeffs.qshift`.
:param discard_level_1: True if level 1 high-pass bands are to be discarded.
"""
# Load bi-orthogonal wavelets
try:
self.biort = _biort(biort)
except TypeError:
self.biort = biort
# Load quarter sample shift wavelets
try:
self.qshift = _qshift(qshift)
except TypeError:
self.qshift = qshift
self.ext_mode = ext_mode
self.discard_level_1 = discard_level_1
def forward(self, X, nlevels=3, include_scale=False):
"""Perform a *n*-level DTCWT decompostion on a 1D column vector *X* (or on
the columns of a matrix *X*).
:param X: 1D real array or 2D real array whose columns are to be transformed
:param nlevels: Number of levels of wavelet decomposition
:returns: A :py:class:`DTCWT.Pyramid`-like object representing the transform result.
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).
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, May 2002
.. codeauthor:: Cian Shaffrey, Cambridge University, May 2002
"""
# Which wavelets are to be used?
biort = self.biort
qshift = self.qshift
# Need this because colfilter and friends assumes input is 2d
X = asfarray(X)
if len(X.shape) == 1:
X = np.atleast_2d(X).T
# 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
L = np.asanyarray(X.shape)
# ensure that X is an even length, thus enabling it to be extended if needs be.
if X.shape[0] % 2 != 0:
raise ValueError('Size of input X must be a multiple of 2')
if nlevels == 0:
if include_scale:
return Pyramid(X, (), ())
else:
return Pyramid(X, ())
# initialise
Yh = [
None,
] * nlevels
if include_scale:
# This is only required if the user specifies scales are to be outputted
Yscale = [
None,
] * nlevels
# Level 1.
Hi = colfilter(X, h1o)
Lo = colfilter(X, h0o)
Yh[0] = Hi[::2, :] + 1j * Hi[1::2, :] # Convert Hi to complex form.
if include_scale:
Yscale[0] = Lo
# Levels 2 and above.
for level in xrange(1, nlevels):
# Check to see if height of Lo is divisable by 4, if not extend.
if Lo.shape[0] % 4 != 0:
Lo = np.vstack((Lo[0, :], Lo, Lo[-1, :]))
Hi = coldfilt(Lo, h1b, h1a)
Lo = coldfilt(Lo, h0b, h0a)
Yh[level] = Hi[::2, :] + 1j * Hi[
1::2, :] # Convert Hi to complex form.
if include_scale:
Yscale[level] = Lo
Yl = Lo
if include_scale:
return Pyramid(Yl, Yh, Yscale)
else:
return Pyramid(Yl, Yh)
def inverse_hu(self, pyramid, gain_mask=None):
"""Perform an *n*-level dual-tree complex wavelet (DTCWT) 1D
reconstruction.
:param pyramid: A :py:class:`DTCWT.Pyramid`-like object containing the transformed signal.
:param gain_mask: Gain to be applied to each subband.
:returns: 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.
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, May 2002
.. codeauthor:: Cian Shaffrey, Cambridge University, May 2002
"""
# Which wavelets are to be used?
biort = self.biort
qshift = self.qshift
Yl = pyramid.lowpass
Yh = pyramid.highpasses
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
""" 此处可以将 hi Lo 拆开 逐层恢复，考虑到卷积是可拆分的 (x1 + x2) * k = x1 * k + x2 * k """
low_band_signal = np.copy(Yl)
high_band_signals = [c2q1d(np.copy(item)) for item in Yh[::-1]]
for i in range(level):
low_band_signal = colifilt(low_band_signal, g0b, g0a)
high_band_signals[i] = colifilt(high_band_signals[i], g1b, g1a)
if low_band_signal.shape[0] != high_band_signals[i + 1].shape[0]:
low_band_signal = low_band_signal[1:-1, ...]
if high_band_signals[i].shape[0] != high_band_signals[i +
1].shape[0]:
high_band_signals[i] = high_band_signals[i][1:-1, ...]
for j in range(i):
high_band_signals[j] = colifilt(high_band_signals[j], g0b, g0a)
if high_band_signals[j].shape[0] != high_band_signals[
i + 1].shape[0]:
high_band_signals[j] = high_band_signals[j][1:-1, ...]
low_band_signal = colfilter(low_band_signal, g0o)
high_band_signals[-1] = colfilter(high_band_signals[-1], g1o)
for i in range(level):
high_band_signals[i] = colfilter(high_band_signals[i], g0o)
return low_band_signal, high_band_signals
def _inverse_ops(self, Yl, Yh, gain_mask=None):
"""Perform an *n*-level dual-tree complex wavelet (DTCWT) 1D
reconstruction.
:param Yl: The lowpass output from a forward transform. Should be a
tensorflow variable.
:param Yh: The tuple of highpass outputs from a forward transform.
Should be tensorflow variables.
:param gain_mask: Gain to be applied to each subband.
:returns: A tf.Variable holding the output
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.
.. codeauthor:: Fergal Cotter <*****@*****.**>, Sep 2017
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, May 2002
.. codeauthor:: Cian Shaffrey, Cambridge University, May 2002
"""
# Which wavelets are to be used?
biort = self.biort
qshift = self.qshift
a = len(Yh) # No of levels.
if gain_mask is None:
gain_mask = np.ones(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
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
# Reconstruct levels 2 and above in reverse order.
Lo = Yl
while level >= 1:
Hi = c2q1d(Yh[level]*gain_mask[level])
Lo = colifilt(Lo, g0b, g0a) + colifilt(Hi, g1b, g1a)
# If Lo is not the same length as the next Therefore we have to clip
# Lo so it is the same height as the next Yh. Yh => t1 was extended.
Lo_shape = Lo.get_shape().as_list()
next_shape = Yh[level-1].get_shape().as_list()
if Lo_shape[1] != 2 * next_shape[1]:
Lo = Lo[:,1:-1]
Lo_shape = Lo.get_shape().as_list()
# Check the row shapes across the entire matrix
if (np.any(np.asanyarray(Lo_shape[1:]) !=
np.asanyarray(next_shape[1:] * np.array((2,1))))):
raise ValueError('Yh sizes are not valid for DTWAVEIFM')
level -= 1
# Reconstruct level 1.
if level == 0:
Hi = c2q1d(Yh[level]*gain_mask[level])
Z = colfilter(Lo,g0o) + colfilter(Hi,g1o)
return Z
def _forward_ops(self, X, nlevels=3):
""" Perform a *n*-level DTCWT-2D decompostion on a 2D matrix *X*.
For column inputs, we still need the input shape to be 3D, but with 1 as
the last dimension.
:param X: 3D real array of size [batch, h, w]
:param nlevels: Number of levels of wavelet decomposition
:param extended: True if a singleton dimension was added at the
beginning of the input. Signal to remove afterwards.
:returns: A tuple of Yl, Yh, Yscale
"""
biort = self.biort
qshift = self.qshift
# 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
# Check the shape and form of the input
if X.dtype not in tf_dtypes:
raise ValueError('X needs to be a tf variable or placeholder')
original_size = X.get_shape().as_list()[1:]
# ############################ Resize #################################
# The next few lines of code check to see if the image is odd in size,
# if so an extra ... row/column will be added to the bottom/right of the
# image
# initial_row_extend = 0
# initial_col_extend = 0
# If the row count of X is not divisible by 2 then we need to
# extend X by adding a row at the bottom
if original_size[0] % 2 != 0:
# X = tf.pad(X, [[0, 0], [0, 1], [0, 0]], 'SYMMETRIC')
raise ValueError('Size of input X must be a multiple of 2')
# extended_size = X.get_shape().as_list()[1:]
if nlevels == 0:
return X, (), ()
# ########################### Initialise ###############################
Yh = [None, ] * nlevels
# This is only required if the user specifies a third output
# component.
Yscale = [None, ] * nlevels
# ############################ Level 1 #################################
# Uses the biorthogonal filters
if nlevels >= 1:
# Do odd top-level filters on cols.
Hi = colfilter(X, h1o)
Lo = colfilter(X, h0o)
# Convert Hi to complex form by taking alternate rows
Yh[0] = tf.cast(Hi[:,::2,:], tf.complex64) + \
1j*tf.cast(Hi[:,1::2,:], tf.complex64)
Yscale[0] = Lo
# ############################ Level 2+ ################################
# Uses the qshift filters
for level in xrange(1, nlevels):
# If the row count of Lo is not divisible by 4 (it will be
# divisible by 2), add 2 extra rows to make it so
if Lo.get_shape().as_list()[1] % 4 != 0:
Lo = tf.pad(Lo, [[0, 0], [1, 1], [0, 0]], 'SYMMETRIC')
# Do even Qshift filters on cols.
Hi = coldfilt(Lo, h1b, h1a)
Lo = coldfilt(Lo, h0b, h0a)
# Convert Hi to complex form by taking alternate rows
Yh[level] = tf.cast(Hi[:,::2,:], tf.complex64) + \
1j * tf.cast(Hi[:,1::2,:], tf.complex64)
Yscale[level] = Lo
Yl = Lo
return Yl, tuple(Yh), tuple(Yscale)
def forward(self, X, nlevels=3, include_scale=False):
"""Perform a *n*-level DTCWT decompostion on a 1D column vector *X* (or on
the columns of a matrix *X*).
:param X: 1D real array or 2D real array whose columns are to be transformed
:param nlevels: Number of levels of wavelet decomposition
:returns: A :py:class:`dtcwt.Pyramid`-like object representing the transform result.
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).
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, May 2002
.. codeauthor:: Cian Shaffrey, Cambridge University, May 2002
"""
# Which wavelets are to be used?
biort = self.biort
qshift = self.qshift
# Need this because colfilter and friends assumes input is 2d
X = asfarray(X)
if len(X.shape) == 1:
X = np.atleast_2d(X).T
# 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
L = np.asanyarray(X.shape)
# ensure that X is an even length, thus enabling it to be extended if needs be.
if X.shape[0] % 2 != 0:
raise ValueError("Size of input X must be a multiple of 2")
if nlevels == 0:
if include_scale:
return Pyramid(X, (), ())
else:
return Pyramid(X, ())
# initialise
Yh = [None] * nlevels
if include_scale:
# This is only required if the user specifies scales are to be outputted
Yscale = [None] * nlevels
# Level 1.
Hi = colfilter(X, h1o)
Lo = colfilter(X, h0o)
Yh[0] = Hi[::2, :] + 1j * Hi[1::2, :] # Convert Hi to complex form.
if include_scale:
Yscale[0] = Lo
# Levels 2 and above.
for level in xrange(1, nlevels):
# Check to see if height of Lo is divisable by 4, if not extend.
if Lo.shape[0] % 4 != 0:
Lo = np.vstack((Lo[0, :], Lo, Lo[-1, :]))
Hi = coldfilt(Lo, h1b, h1a)
Lo = coldfilt(Lo, h0b, h0a)
Yh[level] = Hi[::2, :] + 1j * Hi[1::2, :] # Convert Hi to complex form.
if include_scale:
Yscale[level] = Lo
Yl = Lo
if include_scale:
return Pyramid(Yl, Yh, Yscale)
else:
return Pyramid(Yl, Yh)
def inverse(self, pyramid, gain_mask=None):
"""Perform an *n*-level dual-tree complex wavelet (DTCWT) 1D
reconstruction.
:param pyramid: A :py:class:`dtcwt.Pyramid`-like object containing the transformed signal.
:param gain_mask: Gain to be applied to each subband.
:returns: 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.
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, May 2002
.. codeauthor:: Cian Shaffrey, Cambridge University, May 2002
"""
# Which wavelets are to be used?
biort = self.biort
qshift = self.qshift
Yl = pyramid.lowpass
Yh = pyramid.highpasses
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 inverse(self, pyramid, gain_mask=None):
"""Perform an *n*-level dual-tree complex wavelet (DTCWT) 1D
reconstruction.
:param pyramid: A :py:class:`dtcwt.Pyramid`-like object containing the transformed signal.
:param gain_mask: Gain to be applied to each subband.
:returns: 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.
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, May 2002
.. codeauthor:: Cian Shaffrey, Cambridge University, May 2002
"""
# Which wavelets are to be used?
biort = self.biort
qshift = self.qshift
Yl = pyramid.lowpass
Yh = pyramid.highpasses
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
