def test_wavedecn_shapes_and_size():
wav = pywt.Wavelet('db2')
for data_shape in [(33, ), (64, 32), (1, 15, 30)]:
for axes in [None, 0, -1]:
for mode in pywt.Modes.modes:
coeffs = pywt.wavedecn(np.ones(data_shape),
wav,
mode=mode,
axes=axes)
# verify that the shapes match the coefficient shapes
shapes = pywt.wavedecn_shapes(data_shape,
wav,
mode=mode,
axes=axes)
assert_equal(coeffs[0].shape, shapes[0])
expected_size = coeffs[0].size
for level in range(1, len(coeffs)):
for k, v in coeffs[level].items():
expected_size += v.size
assert_equal(shapes[level][k], v.shape)
# size can be determined from either the shapes or coeffs
size = pywt.wavedecn_size(shapes)
assert_equal(size, expected_size)
size = pywt.wavedecn_size(coeffs)
assert_equal(size, expected_size)
def test_wavedecn_shapes_and_size():
wav = pywt.Wavelet('db2')
for data_shape in [(33, ), (64, 32), (1, 15, 30)]:
for axes in [None, 0, -1]:
for mode in pywt.Modes.modes:
coeffs = pywt.wavedecn(np.ones(data_shape), wav,
mode=mode, axes=axes)
# verify that the shapes match the coefficient shapes
shapes = pywt.wavedecn_shapes(data_shape, wav,
mode=mode, axes=axes)
assert_equal(coeffs[0].shape, shapes[0])
expected_size = coeffs[0].size
for level in range(1, len(coeffs)):
for k, v in coeffs[level].items():
expected_size += v.size
assert_equal(shapes[level][k], v.shape)
# size can be determined from either the shapes or coeffs
size = pywt.wavedecn_size(shapes)
assert_equal(size, expected_size)
size = pywt.wavedecn_size(coeffs)
assert_equal(size, expected_size)
def waveletDenoise(data):
# data is num_neurons x time_frames
wavelet = pywt.Wavelet('db4')
# Determine the maximum number of possible levels for image
dlen = wavelet.dec_len
wavelet_levels = pywt.dwt_max_level(data.shape[1], wavelet)
# Skip coarsest wavelet scales (see Notes in docstring).
wavelet_levels = max(wavelet_levels - 3, 1)
data_denoise = np.zeros(np.shape(data))
shift = 4
for c in np.arange(-shift, shift + 1):
data_shift = np.roll(data, c, 1)
for i in range(np.shape(data)[0]):
coeffs = pywt.wavedecn(data_shift[i, :],
wavelet=wavelet,
level=wavelet_levels)
# Detail coefficients at each decomposition level
dcoeffs = coeffs[1:]
detail_coeffs = dcoeffs[-1]['d']
# rescaling using a single estimation of level noise based on first level coefficients.
# Consider regions with detail coefficients exactly zero to be masked out
# detail_coeffs = detail_coeffs[np.nonzero(detail_coeffs)]
# 75th quantile of the underlying, symmetric noise distribution
denom = scipy.stats.norm.ppf(0.75)
sigma = np.median(np.abs(detail_coeffs)) / denom
np.shape(sigma)
sigma_mat = np.tile(sigma, (wavelet_levels, 1))
np.shape(sigma_mat)
tot_num_coeffs = pywt.wavedecn_size(coeffs)
# universal threshold
threshold = np.sqrt(2 * np.log(tot_num_coeffs))
threshold = sigma * threshold
denoised_detail = [{
key: pywt.threshold(level[key], value=threshold, mode='hard')
for key in level
} for level in dcoeffs]
# Dict of unique threshold coefficients for each detail coeff. array
denoised_coeffs = [coeffs[0]] + denoised_detail
data_denoise[i, :] = data_denoise[i, :] + np.roll(
pywt.waverecn(denoised_coeffs, wavelet),
-c)[:data_denoise.shape[1]]
data_denoise = data_denoise / (2 * shift + 1)
return data_denoise
def __init__(self,
space,
wavelet,
nlevels,
variant,
pad_mode='constant',
pad_const=0,
impl='pywt',
axes=None):
"""Initialize a new instance.
Parameters
----------
space : `DiscreteLp`
Domain of the forward wavelet transform (the "image domain").
In the case of ``variant in ('inverse', 'adjoint')``, this
space is the range of the operator.
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.
Possible wavelet families are:
``'haar'``: Haar
``'db'``: Daubechies
``'sym'``: Symlets
``'coif'``: Coiflets
``'bior'``: Biorthogonal
``'rbio'``: Reverse biorthogonal
``'dmey'``: Discrete FIR approximation of the Meyer wavelet
variant : {'forward', 'inverse', 'adjoint'}
Wavelet transform variant to be created.
nlevels : positive int, optional
Number of scaling levels to be used in the decomposition. The
maximum number of levels can be calculated with
`pywt.dwtn_max_level`.
Default: Use maximum number of levels.
pad_mode : string, optional
Method to be used to extend the signal.
``'constant'``: Fill with ``pad_const``.
``'symmetric'``: Reflect at the boundaries, not repeating the
outmost values.
``'periodic'``: Fill in values from the other side, keeping
the order.
``'order0'``: Extend constantly with the outmost values
(ensures continuity).
``'order1'``: Extend with constant slope (ensures continuity of
the first derivative). This requires at least 2 values along
each axis where padding is applied.
``'pywt_per'``: like ``'periodic'``-padding but gives the smallest
possible number of decomposition coefficients.
Only available with ``impl='pywt'``, See ``pywt.Modes.modes``.
``'reflect'``: Reflect at the boundary, without repeating the
outmost values.
``'antisymmetric'``: Anti-symmetric variant of ``symmetric``.
``'antireflect'``: Anti-symmetric variant of ``reflect``.
For reference, the following table compares the naming conventions
for the modes in ODL vs. PyWavelets::
======================= ==================
ODL PyWavelets
======================= ==================
symmetric symmetric
reflect reflect
order1 smooth
order0 constant
constant, pad_const=0 zero
periodic periodic
pywt_per periodization
antisymmetric antisymmetric
antireflect antireflect
======================= ==================
See `signal extension modes`_ for an illustration of the modes
(under the PyWavelets naming conventions).
pad_const : float, optional
Constant value to use if ``pad_mode == 'constant'``. Ignored
otherwise. Constants other than 0 are not supported by the
``pywt`` back-end.
impl : {'pywt'}, optional
Back-end for the wavelet transform.
axes : sequence of ints, optional
Axes over which the DWT that created ``coeffs`` was performed. The
default value of ``None`` corresponds to all axes. When not all
axes are included this is analagous to a batch transform in
``len(axes)`` dimensions looped over the non-transformed axes. In
orther words, filtering and decimation does not occur along any
axes not in ``axes``.
References
----------
.. _signal extension modes:
https://pywavelets.readthedocs.io/en/latest/ref/signal-extension-modes.html
"""
if not isinstance(space, DiscreteLp):
raise TypeError('`space` {!r} is not a `DiscreteLp` instance.'
''.format(space))
self.__impl, impl_in = str(impl).lower(), impl
if self.impl not in _SUPPORTED_WAVELET_IMPLS:
raise ValueError("`impl` '{}' not supported".format(impl_in))
if axes is None:
axes = tuple(range(space.ndim))
elif np.isscalar(axes):
axes = (axes, )
elif len(axes) > space.ndim:
raise ValueError("Too many axes.")
self.axes = tuple(axes)
if nlevels is None:
nlevels = pywt.dwtn_max_level(space.shape, wavelet, self.axes)
self.__nlevels, nlevels_in = int(nlevels), nlevels
if self.nlevels != nlevels_in:
raise ValueError('`nlevels` must be integer, got {}'
''.format(nlevels_in))
self.__impl, impl_in = str(impl).lower(), impl
if self.impl not in _SUPPORTED_WAVELET_IMPLS:
raise ValueError("`impl` '{}' not supported".format(impl_in))
self.__wavelet = getattr(wavelet, 'name', str(wavelet).lower())
self.__pad_mode = str(pad_mode).lower()
self.__pad_const = space.field.element(pad_const)
if self.impl == 'pywt':
self.pywt_pad_mode = pywt_pad_mode(pad_mode, pad_const)
self.pywt_wavelet = pywt_wavelet(self.wavelet)
# determine coefficient shapes (without running wavedecn)
self._coeff_shapes = pywt.wavedecn_shapes(space.shape,
wavelet,
mode=self.pywt_pad_mode,
level=self.nlevels,
axes=self.axes)
# precompute slices into the (raveled) coeffs
self._coeff_slices = precompute_raveled_slices(self._coeff_shapes)
coeff_size = pywt.wavedecn_size(self._coeff_shapes)
coeff_space = space.tspace_type(coeff_size, dtype=space.dtype)
else:
raise RuntimeError("bad `impl` '{}'".format(self.impl))
variant, variant_in = str(variant).lower(), variant
if variant not in ('forward', 'inverse', 'adjoint'):
raise ValueError("`variant` '{}' not understood"
"".format(variant_in))
self.__variant = variant
if variant == 'forward':
super(WaveletTransformBase, self).__init__(domain=space,
range=coeff_space,
linear=True)
else:
super(WaveletTransformBase, self).__init__(domain=coeff_space,
range=space,
linear=True)
+-------------------------------+-------------------------------+ """ cam = pywt.data.camera() coeffs = pywt.wavedecn(cam, wavelet="db2", level=3) # Concatenating all coefficients into a single n-d array arr, coeff_slices = pywt.coeffs_to_array(coeffs) # Splitting concatenated coefficient array back into its components coeffs_from_arr = pywt.array_to_coeffs(arr, coeff_slices) cam_recon = pywt.waverecn(coeffs_from_arr, wavelet='db2') # Raveling coefficients to a 1D array arr, coeff_slices, coeff_shapes = pywt.ravel_coeffs(coeffs) # Unraveling coefficients from a 1D array coeffs_from_arr = pywt.unravel_coeffs(arr, coeff_slices, coeff_shapes) cam_recon2 = pywt.waverecn(coeffs_from_arr, wavelet='db2') # Multilevel: n-d coefficient shapes shapes = pywt.wavedecn_shapes((64, 32), 'db2', mode='periodization') # Multilevel: Total size of all coefficients size = pywt.wavedecn_size(shapes) print(size) print()
