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 dtwaveifm3(Yl, Yh, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, ext_mode=4):
"""Perform an *n*-level dual-tree complex wavelet (DTCWT) 3D
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 ext_mode: Extension mode. See below.
:returns Z: Reconstructed real image matrix.
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).
There are two values for *ext_mode*, either 4 or 8. If *ext_mode* = 4,
check whether 1st level is divisible by 2 (if not we raise a
``ValueError``). Also check whether from 2nd level onwards, the coefs can
be divided by 4. If any dimension size is not a multiple of 4, append extra
coefs by repeating the edges. If *ext_mode* = 8, check whether 1st level is
divisible by 4 (if not we raise a ``ValueError``). Also check whether from
2nd level onwards, the coeffs can be divided by 8. If any dimension size is
not a multiple of 8, append extra coeffs by repeating the edges twice.
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 = dtwaveifm3(Yl, Yh, 'near_sym_b', 'qshift_b')
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Huizhong Chen, Jan 2009
.. codeauthor:: Nick Kingsbury, Cambridge University, July 1999.
"""
# 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
X = Yl
nlevels = len(Yh)
# level is 0-indexed but interpreted starting from the *last* level
for level in xrange(nlevels):
# Transform
if level == nlevels-1: # non-obviously this is the 'first' level
if Yh[-level-1] is None:
Yl = _level1_ifm_no_highpass(Yl, g0o, g1o)
else:
Yl = _level1_ifm(Yl, Yh[-level-1], g0o, g1o)
else:
# Gracefully handle the Yh[0] is None case.
if Yh[-level-2] is not None:
prev_shape = Yh[-level-2].shape
else:
prev_shape = np.array(Yh[-level-1].shape) * 2
Yl = _level2_ifm(Yl, Yh[-level-1], g0a, g0b, g1a, g1b, ext_mode, prev_shape)
return Yl
def dtwavexfm(X,
nlevels=3,
biort=DEFAULT_BIORT,
qshift=DEFAULT_QSHIFT,
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
:param biort: Level 1 wavelets to use. See :py:func:`biort`.
:param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.
:returns Yl: The real lowpass image from the final level
:returns Yh: A tuple containing the (N, M, 6) shape complex highpass subimages for each level.
:returns Yscale: If *include_scale* is True, a tuple containing real lowpass coefficients for every scale.
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 5-level transform on the real image X using the 13,19-tap
# filters for level 1 and the Q-shift 14-tap filters for levels >= 2.
Yl, Yh = dtwavexfm(X,5,'near_sym_b','qshift_b')
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, May 2002
.. codeauthor:: Cian Shaffrey, Cambridge University, May 2002
"""
# 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 X, (), ()
else:
return 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 Yl, Yh, Yscale
else:
return Yl, Yh
def dtwavexfm(X, nlevels=3, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, 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
:param biort: Level 1 wavelets to use. See :py:func:`biort`.
:param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.
:returns Yl: The real lowpass image from the final level
:returns Yh: A tuple containing the (N, M, 6) shape complex highpass subimages for each level.
:returns Yscale: If *include_scale* is True, a tuple containing real lowpass coefficients for every scale.
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 5-level transform on the real image X using the 13,19-tap
# filters for level 1 and the Q-shift 14-tap filters for levels >= 2.
Yl, Yh = dtwavexfm(X,5,'near_sym_b','qshift_b')
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, May 2002
.. codeauthor:: Cian Shaffrey, Cambridge University, May 2002
"""
# 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 X, (), ()
else:
return 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 Yl, Yh, Yscale
else:
return Yl, Yh
def dtwavexfm3(X, nlevels=3, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, ext_mode=4, discard_level_1=False):
"""Perform a *n*-level DTCWT-3D decompostion on a 3D matrix *X*.
:param X: 3D real array-like object
:param nlevels: Number of levels of wavelet decomposition
:param biort: Level 1 wavelets to use. See :py:func:`biort`.
:param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.
:param ext_mode: Extension mode. See below.
:param discard_level_1: True if level 1 high-pass bands are to be discarded.
:returns Yl: The real lowpass image from the final level
:returns Yh: A tuple containing the complex highpass subimages for each level.
Each element of *Yh* is a 4D complex array with the 4th dimension having
size 28. The 3D slice ``Yh[l][:,:,:,d]`` corresponds to the complex higpass
coefficients for direction d at level l where d and l are both 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).
There are two values for *ext_mode*, either 4 or 8. If *ext_mode* = 4,
check whether 1st level is divisible by 2 (if not we raise a
``ValueError``). Also check whether from 2nd level onwards, the coefs can
be divided by 4. If any dimension size is not a multiple of 4, append extra
coefs by repeating the edges. If *ext_mode* = 8, check whether 1st level is
divisible by 4 (if not we raise a ``ValueError``). Also check whether from
2nd level onwards, the coeffs can be divided by 8. If any dimension size is
not a multiple of 8, append extra coeffs by repeating the edges twice.
If *discard_level_1* is True the highpass coefficients at level 1 will be
discarded. (And, in fact, will never be calculated.) This turns the
transform from being 8:1 redundant to being 1:1 redundant at the cost of
no-longer allowing perfect reconstruction. If this option is selected then
`Yh[0]` will be `None`. Note that :py:func:`dtwaveifm3` will accepts
`Yh[0]` being `None` and will treat it as being zero.
Example::
# Performs a 3-level transform on the real 3D array X using the 13,19-tap
# filters for level 1 and the Q-shift 14-tap filters for levels >= 2.
Yl, Yh = dtwavexfm3(X, 3, 'near_sym_b', 'qshift_b')
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Huizhong Chen, Jan 2009
.. codeauthor:: Nick Kingsbury, Cambridge University, July 1999.
"""
X = np.atleast_3d(asfarray(X))
# 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 value of ext_mode. TODO: this should really be an enum :S
if ext_mode != 4 and ext_mode != 8:
raise ValueError('ext_mode must be one of 4 or 8')
Yl = X
Yh = [None,] * nlevels
# level is 0-indexed
for level in xrange(nlevels):
# Transform
if level == 0 and discard_level_1:
Yl = _level1_xfm_no_highpass(Yl, h0o, h1o, ext_mode)
elif level == 0 and not discard_level_1:
Yl, Yh[level] = _level1_xfm(Yl, h0o, h1o, ext_mode)
else:
Yl, Yh[level] = _level2_xfm(Yl, h0a, h0b, h1a, h1b, ext_mode)
return Yl, tuple(Yh)
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 dtwavexfm2(X, nlevels=3, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, include_scale=False):
"""Perform a *n*-level DTCWT-2D decompostion on a 2D matrix *X*.
:param X: 2D real array
:param nlevels: Number of levels of wavelet decomposition
:param biort: Level 1 wavelets to use. See :py:func:`biort`.
:param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.
:returns Yl: The real lowpass image from the final level
:returns Yh: A tuple containing the complex highpass subimages for each level.
:returns Yscale: If *include_scale* is True, a tuple containing real lowpass coefficients for every scale.
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 transform on the real image X using the 13,19-tap
# filters for level 1 and the Q-shift 14-tap filters for levels >= 2.
Yl, Yh = dtwavexfm2(X, 3, 'near_sym_b', 'qshift_b')
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, Sept 2001
.. codeauthor:: Cian Shaffrey, Cambridge University, Sept 2001
"""
X = np.atleast_2d(asfarray(X))
# 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
original_size = X.shape
if len(X.shape) >= 3:
raise ValueError('The entered image is {0}, please enter each image slice separately.'.
format('x'.join(list(str(s) for s in X.shape))))
# 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 #initialise
initial_col_extend = 0
if original_size[0] % 2 != 0:
# if X.shape[0] is not divisable by 2 then we need to extend X by adding a row at the bottom
X = np.vstack((X, X[[-1],:])) # Any further extension will be done in due course.
initial_row_extend = 1
if original_size[1] % 2 != 0:
# if X.shape[1] is not divisable by 2 then we need to extend X by adding a col to the left
X = np.hstack((X, X[:,[-1]]))
initial_col_extend = 1
extended_size = X.shape
if nlevels == 0:
if include_scale:
return X, (), ()
else:
return X, ()
# initialise
Yh = [None,] * nlevels
if include_scale:
# this is only required if the user specifies a third output component.
Yscale = [None,] * nlevels
complex_dtype = appropriate_complex_type_for(X)
if nlevels >= 1:
# Do odd top-level filters on cols.
Lo = colfilter(X,h0o).T
Hi = colfilter(X,h1o).T
# Do odd top-level filters on rows.
LoLo = colfilter(Lo,h0o).T
Yh[0] = np.zeros((LoLo.shape[0] >> 1, LoLo.shape[1] >> 1, 6), dtype=complex_dtype)
Yh[0][:,:,[0, 5]] = q2c(colfilter(Hi,h0o).T) # Horizontal pair
Yh[0][:,:,[2, 3]] = q2c(colfilter(Lo,h1o).T) # Vertical pair
Yh[0][:,:,[1, 4]] = q2c(colfilter(Hi,h1o).T) # Diagonal pair
if include_scale:
Yscale[0] = LoLo
for level in xrange(1, nlevels):
row_size, col_size = LoLo.shape
if row_size % 4 != 0:
# Extend by 2 rows if no. of rows of LoLo are not divisable by 4
LoLo = np.vstack((LoLo[[0],:], LoLo, LoLo[[-1],:]))
if col_size % 4 != 0:
# Extend by 2 cols if no. of cols of LoLo are not divisable by 4
LoLo = np.hstack((LoLo[:,[0]], LoLo, LoLo[:,[-1]]))
# Do even Qshift filters on rows.
Lo = coldfilt(LoLo,h0b,h0a).T
Hi = coldfilt(LoLo,h1b,h1a).T
# Do even Qshift filters on columns.
LoLo = coldfilt(Lo,h0b,h0a).T
Yh[level] = np.zeros((LoLo.shape[0]>>1, LoLo.shape[1]>>1, 6), dtype=complex_dtype)
Yh[level][:,:,[0, 5]] = q2c(coldfilt(Hi,h0b,h0a).T) # Horizontal
Yh[level][:,:,[2, 3]] = q2c(coldfilt(Lo,h1b,h1a).T) # Vertical
Yh[level][:,:,[1, 4]] = q2c(coldfilt(Hi,h1b,h1a).T) # Diagonal
if include_scale:
Yscale[0] = LoLo
Yl = LoLo
if initial_row_extend == 1 and initial_col_extend == 1:
logging.warn('The image entered is now a {0} NOT a {1}.'.format(
'x'.join(list(str(s) for s in extended_size)),
'x'.join(list(str(s) for s in original_size))))
logging.warn(
'The bottom row and rightmost column have been duplicated, prior to decomposition.')
if initial_row_extend == 1 and initial_col_extend == 0:
logging.warn('The image entered is now a {0} NOT a {1}.'.format(
'x'.join(list(str(s) for s in extended_size)),
'x'.join(list(str(s) for s in original_size))))
logging.warn(
'The bottom row has been duplicated, prior to decomposition.')
if initial_row_extend == 0 and initial_col_extend == 1:
logging.warn('The image entered is now a {0} NOT a {1}.'.format(
'x'.join(list(str(s) for s in extended_size)),
'x'.join(list(str(s) for s in original_size))))
logging.warn(
'The rightmost column has been duplicated, prior to decomposition.')
if include_scale:
return Yl, tuple(Yh), tuple(Yscale)
else:
return Yl, tuple(Yh)
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 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 dtwavexfm2(X, nlevels=3, biort=DEFAULT_BIORT, qshift=DEFAULT_QSHIFT, include_scale=False):
"""Perform a *n*-level DTCWT-2D decompostion on a 2D matrix *X*.
:param X: 2D real array
:param nlevels: Number of levels of wavelet decomposition
:param biort: Level 1 wavelets to use. See :py:func:`biort`.
:param qshift: Level >= 2 wavelets to use. See :py:func:`qshift`.
:returns Yl: The real lowpass image from the final level
:returns Yh: A tuple containing the complex highpass subimages for each level.
:returns Yscale: If *include_scale* is True, a tuple containing real lowpass coefficients for every scale.
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 transform on the real image X using the 13,19-tap
# filters for level 1 and the Q-shift 14-tap filters for levels >= 2.
Yl, Yh = dtwavexfm2(X, 3, 'near_sym_b', 'qshift_b')
.. codeauthor:: Rich Wareham <*****@*****.**>, Aug 2013
.. codeauthor:: Nick Kingsbury, Cambridge University, Sept 2001
.. codeauthor:: Cian Shaffrey, Cambridge University, Sept 2001
"""
X = np.atleast_2d(asfarray(X))
# 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
original_size = X.shape
if len(X.shape) >= 3:
raise ValueError(
"The entered image is {0}, please enter each image slice separately.".format(
"x".join(list(str(s) for s in X.shape))
)
)
# 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 # initialise
initial_col_extend = 0
if original_size[0] % 2 != 0:
# if X.shape[0] is not divisable by 2 then we need to extend X by adding a row at the bottom
X = np.vstack((X, X[[-1], :])) # Any further extension will be done in due course.
initial_row_extend = 1
if original_size[1] % 2 != 0:
# if X.shape[1] is not divisable by 2 then we need to extend X by adding a col to the left
X = np.hstack((X, X[:, [-1]]))
initial_col_extend = 1
extended_size = X.shape
if nlevels == 0:
if include_scale:
return X, (), ()
else:
return X, ()
# initialise
Yh = [None] * nlevels
if include_scale:
# this is only required if the user specifies a third output component.
Yscale = [None] * nlevels
complex_dtype = appropriate_complex_type_for(X)
if nlevels >= 1:
# Do odd top-level filters on cols.
Lo = colfilter(X, h0o).T
Hi = colfilter(X, h1o).T
# Do odd top-level filters on rows.
LoLo = colfilter(Lo, h0o).T
Yh[0] = np.zeros((LoLo.shape[0] >> 1, LoLo.shape[1] >> 1, 6), dtype=complex_dtype)
Yh[0][:, :, [0, 5]] = q2c(colfilter(Hi, h0o).T) # Horizontal pair
Yh[0][:, :, [2, 3]] = q2c(colfilter(Lo, h1o).T) # Vertical pair
Yh[0][:, :, [1, 4]] = q2c(colfilter(Hi, h1o).T) # Diagonal pair
if include_scale:
Yscale[0] = LoLo
for level in xrange(1, nlevels):
row_size, col_size = LoLo.shape
if row_size % 4 != 0:
# Extend by 2 rows if no. of rows of LoLo are not divisable by 4
LoLo = np.vstack((LoLo[[0], :], LoLo, LoLo[[-1], :]))
if col_size % 4 != 0:
# Extend by 2 cols if no. of cols of LoLo are not divisable by 4
LoLo = np.hstack((LoLo[:, [0]], LoLo, LoLo[:, [-1]]))
# Do even Qshift filters on rows.
Lo = coldfilt(LoLo, h0b, h0a).T
Hi = coldfilt(LoLo, h1b, h1a).T
# Do even Qshift filters on columns.
LoLo = coldfilt(Lo, h0b, h0a).T
Yh[level] = np.zeros((LoLo.shape[0] >> 1, LoLo.shape[1] >> 1, 6), dtype=complex_dtype)
Yh[level][:, :, [0, 5]] = q2c(coldfilt(Hi, h0b, h0a).T) # Horizontal
Yh[level][:, :, [2, 3]] = q2c(coldfilt(Lo, h1b, h1a).T) # Vertical
Yh[level][:, :, [1, 4]] = q2c(coldfilt(Hi, h1b, h1a).T) # Diagonal
if include_scale:
Yscale[0] = LoLo
Yl = LoLo
if initial_row_extend == 1 and initial_col_extend == 1:
logging.warn(
"The image entered is now a {0} NOT a {1}.".format(
"x".join(list(str(s) for s in extended_size)), "x".join(list(str(s) for s in original_size))
)
)
logging.warn("The bottom row and rightmost column have been duplicated, prior to decomposition.")
if initial_row_extend == 1 and initial_col_extend == 0:
logging.warn(
"The image entered is now a {0} NOT a {1}.".format(
"x".join(list(str(s) for s in extended_size)), "x".join(list(str(s) for s in original_size))
)
)
logging.warn("The bottom row has been duplicated, prior to decomposition.")
if initial_row_extend == 0 and initial_col_extend == 1:
logging.warn(
"The image entered is now a {0} NOT a {1}.".format(
"x".join(list(str(s) for s in extended_size)), "x".join(list(str(s) for s in original_size))
)
)
logging.warn("The rightmost column has been duplicated, prior to decomposition.")
if include_scale:
return Yl, tuple(Yh), tuple(Yscale)
else:
return Yl, tuple(Yh)