def _wavelet_threshold(img, wavelet, threshold=None, sigma=None, mode='soft'):
"""Performs wavelet denoising.
Parameters
----------
img : ndarray (2d or 3d) of ints, uints or floats
Input data to be denoised. `img` can be of any numeric type,
but it is cast into an ndarray of floats for the computation
of the denoised image.
wavelet : string
The type of wavelet to perform. Can be any of the options
pywt.wavelist outputs. For example, this may be any of ``{db1, db2,
db3, db4, haar}``.
sigma : float, optional
The standard deviation of the noise. The noise is estimated when sigma
is None (the default) by the method in [2]_.
threshold : float, optional
The thresholding value. All wavelet coefficients less than this value
are set to 0. The default value (None) uses the SureShrink method found
in [1]_ to remove noise.
mode : {'soft', 'hard'}, optional
An optional argument to choose the type of denoising performed. It
noted that choosing soft thresholding given additive noise finds the
best approximation of the original image.
Returns
-------
out : ndarray
Denoised image.
References
----------
.. [1] Chang, S. Grace, Bin Yu, and Martin Vetterli. "Adaptive wavelet
thresholding for image denoising and compression." Image Processing,
IEEE Transactions on 9.9 (2000): 1532-1546.
DOI: 10.1109/83.862633
.. [2] D. L. Donoho and I. M. Johnstone. "Ideal spatial adaptation
by wavelet shrinkage." Biometrika 81.3 (1994): 425-455.
DOI: 10.1093/biomet/81.3.425
"""
coeffs = pywt.wavedecn(img, wavelet=wavelet)
detail_coeffs = coeffs[-1]['d' * img.ndim]
if sigma is None:
# Estimates via the noise via method in [2]
sigma = np.median(np.abs(detail_coeffs)) / 0.67448975019608171
if threshold is None:
# The BayesShrink threshold from [1]_ in docstring
threshold = sigma**2 / np.sqrt(max(img.var() - sigma**2, 0))
denoised_detail = [{key: pywt.threshold(level[key], value=threshold,
mode=mode) for key in level} for level in coeffs[1:]]
denoised_root = pywt.threshold(coeffs[0], value=threshold, mode=mode)
denoised_coeffs = [denoised_root] + [d for d in denoised_detail]
return pywt.waverecn(denoised_coeffs, wavelet)
def uncompress_image(compressed_image, level, im_shape):
# Breaking Compressed Wavlet of Image into RGB Layers (Wavlet Compression works on 2D arrays only)
arr_r_compressed = compressed_image[:, :, 0]
arr_g_compressed = compressed_image[:, :, 1]
arr_b_compressed = compressed_image[:, :, 2]
x_shape, y_shape = im_shape
slices = generate_wavlet_slices(x_shape, y_shape, level=level)
# Converting Compressed Coefficients back into Original Wavlet form (which the pywt library can work with)
r_coeff = pywt.array_to_coeffs(arr_r_compressed,
slices,
output_format='wavedecn')
g_coeff = pywt.array_to_coeffs(arr_g_compressed,
slices,
output_format='wavedecn')
b_coeff = pywt.array_to_coeffs(arr_b_compressed,
slices,
output_format='wavedecn')
# Using PYWT to uncompress the wavlet coefficients back into their image form
r_reconstructed = pywt.waverecn(r_coeff, 'db2',
mode='periodization').astype(np.uint8)
g_reconstructed = pywt.waverecn(g_coeff, 'db2',
mode='periodization').astype(np.uint8)
b_reconstructed = pywt.waverecn(b_coeff, 'db2',
mode='periodization').astype(np.uint8)
# Stacking the uncompressed R. G. B. images into the final RGB image
reconstructed_im = (np.stack(
(r_reconstructed, g_reconstructed, b_reconstructed),
2)).astype(np.uint8)
return reconstructed_im
def wavelet_based_BG_subtraction(image, num_levels, noise_lvl):
coeffs = wavedecn(image, 'db1', level=None) #decomposition
coeffs2 = coeffs.copy()
for BGlvl in range(1, num_levels):
coeffs[-BGlvl] = {
k: np.zeros_like(v)
for k, v in coeffs[-BGlvl].items()
} #set lvl 1 details to zero
Background = waverecn(coeffs, 'db1') #reconstruction
del coeffs
BG_unfiltered = Background
Background = gaussian_filter(
Background, sigma=2**num_levels) #gaussian filter sigma = 2^#lvls
coeffs2[0] = np.ones_like(coeffs2[0]) #set approx to one (constant)
for lvl in range(1, np.size(coeffs2) - noise_lvl):
coeffs2[lvl] = {k: np.zeros_like(v)
for k, v in coeffs2[lvl].items()
} #keep first detail lvl only
Noise = waverecn(coeffs2, 'db1') #reconstruction
del coeffs2
return Background, Noise, BG_unfiltered
def test_waverecn_empty_coeff():
coeffs = [np.ones((2, 2, 2)), {}, {}]
assert_equal(pywt.waverecn(coeffs, 'db1').shape, (8, 8, 8))
assert_equal(pywt.waverecn(coeffs, 'db1').shape, (8, 8, 8))
coeffs = [np.ones((2, 2, 2)), {}, {'daa': np.ones((4, 4, 4))}]
coeffs = [np.ones((2, 2, 2)), {}, {}, {'daa': np.ones((8, 8, 8))}]
assert_equal(pywt.waverecn(coeffs, 'db1').shape, (16, 16, 16))
def test_waverecn_empty_coeff():
coeffs = [np.ones((2, 2, 2)), {}, {}]
assert_equal(pywt.waverecn(coeffs, 'db1').shape, (8, 8, 8))
assert_equal(pywt.waverecn(coeffs, 'db1').shape, (8, 8, 8))
coeffs = [np.ones((2, 2, 2)), {}, {'daa': np.ones((4, 4, 4))}]
coeffs = [np.ones((2, 2, 2)), {}, {}, {'daa': np.ones((8, 8, 8))}]
assert_equal(pywt.waverecn(coeffs, 'db1').shape, (16, 16, 16))
def inverse(self, m, wv = 'db4'):
msyn = np.zeros(mesh.nC)
coeff_wv = pywt.wavedecn(msyn.reshape(self.mesh.nCx,self.mesh.nCy,order = 'F'),wv, mode = 'per')
array_wv = pywt.coeffs_to_array(coeff_wv)
coeff_back = pywt.array_to_coeffs(m.reshape(array_wv[0].shape, order = 'F'),array_wv[1])
coeff_m = pywt.waverecn(coeff_back,wv, mode = 'per')
return Utils.mkvc(coeff_m)
def apply_dwt_filter(y, dwt_type, dwt_level, dwt_thresh_func, dwt_thresh_type):
coeffs = pywt.wavedecn(y, dwt_type, level=dwt_level)
for i in range(1, dwt_level + 1):
coeffs[i]["d"] = pywt.threshold(
coeffs[i]["d"], thselect(coeffs[i]["d"], dwt_thresh_type),
dwt_thresh_func)
return (pywt.waverecn(coeffs, dwt_type))
def dwt(self):
#imLists = [IMAGEPATH + "a01_1.tif", IMAGEPATH + "a01_2.tif"]
start = time.time()
self.show_Image_DWt(self.image1)
self.show_Image_DWt(self.image2)
# show_DWt1D()
coeffs = self.calculate_coeffs(self.image1)
arr, coeff_slices = pywt.coeffs_to_array(coeffs)
#show_DWt1D(coeffs)
# show_Image_DWt(coeffs,target)
#self.show_DWt1D()
coeffs2 = self.calculate_coeffs(self.image2)
arr2, coeff_slices2 = pywt.coeffs_to_array(coeffs2)
startPCA = time.time()
# p=PCA()
#array = p.PCA(arr, arr2)#FusionMethod
f = Fusion(arr, arr2)
array = f.PCA()
endPCA = time.time()
print('Gesamtzeit PCA: {:5.3f}s'.format(endPCA - startPCA))
coeffs_from_arr = pywt.array_to_coeffs(array,
coeff_slices,
output_format='wavedecn')
#self.show_DWt1D()
self.target = pywt.waverecn(coeffs_from_arr, wavelet='db1')
self.plot()
end = time.time()
print('Gesamtzeit DWT: {:5.3f}s'.format((end - start) -
(endPCA - startPCA)))
print('Gesamtzeit DWT and PCA: {:5.3f}s'.format(end - start))
return self.target
def decomp(cA, wavelet, levels, mode='constant', omissions=([], False)):
"""
n-dimensional discrete wavelet decompisition and reconstruction
Parameters
----------
cA : array_like
n-dimensional array with input data.
wavelet : Wavelet object or name string
Wavelet to use.
levels : int
The number of decomposition steps to perform.
mode : string, optional
The mode of signal padding, defaults to constant
omissions: tuple(list, bool), optional
List of DETAIL levels to omit, if bool is true omit cA
Returns
-------
nD array of reconstructed data.
"""
if omissions[0] and max(omissions[0]) > levels:
raise ValueError(
"Omission level %d is too high. Maximum allowed is %d." %
(max(omissions[0]), levels))
coeffs = pywt.wavedecn(cA, wavelet, level=levels, mode=mode)
coeffs = omit(coeffs, omissions)
return pywt.waverecn(coeffs, wavelet, mode=mode)
def calc_wavelet_th(line, wavelet_name, count_process, max_process, sgm_n,
coef_m, smoothing):
len_line = len(line)
rep_line = line[::-1] + line[::] + line[::-1]
coeffs = pywt.wavedecn(rep_line, wavelet_name[count_process])
list_, sep_ = pywt.coeffs_to_array(coeffs)
m_max = int(np.log2(len(list_))) ### m(frequency) filter ###
for m in range(1, m_max + 1):
for n in range(2**(m_max - m), 2**(m_max - m) * 2):
if m > m_max * coef_m[count_process] and n != 0:
list_[n] = 0
lambda_ = np.sqrt(2.0 * np.log(
len(rep_line))) * sgm_n[count_process] ### n(location) filter ##
# plt.plot(np.arange(len(list_)),list_);plt.hlines(lambda_,xmin=0,xmax=len(list_));
list_ = [
x if (i < len(list_) * 0.01 or np.abs(x) > lambda_) else 0
for i, x in enumerate(list_)
]
# plt.plot(np.arange(len(list_)),list_);plt.hlines(-lambda_,xmin=0,xmax=len(list_));plt.show();
coeffs = pywt.array_to_coeffs(list_, sep_)
reline = pywt.waverecn(coeffs, wavelet_name[count_process])
# plt.plot(np.arange(len(reline)),reline);plt.plot(np.arange(len(rep_line)),rep_line);plt.show();
if count_process != max_process - 1:
res = calc_wavelet_th(list(reline[len_line:len_line * 2]),
wavelet_name, count_process + 1, max_process,
sgm_n, coef_m, smoothing)
else:
if smoothing:
res = calc_wavelet_smooth(list(reline[len_line:len_line * 2]),
'Haar', 3)
else:
res = list(reline[len_line:len_line * 2])
return res
def adj_op(self, coeffs):
"""
Define the wavelet adjoint operator.
This method returns the reconstructed image.
Parameters
----------
coeffs: np.ndarray
the wavelet coefficients.
Returns
-------
data: np.ndarray((m, n)) or np.ndarray((m, n, p))
the 2D or 3D reconstructed data.
"""
self.coeffs = coeffs
if self.undecimated:
coeffs_dict = self.unflatten(coeffs, self.coeffs_shape)
data = pywt.iswtn(coeffs_dict, self.pywt_transform)
else:
coeffs_dict = self.unflatten(coeffs, self.coeffs_shape)
data = pywt.waverecn(coeffs=coeffs_dict,
wavelet=self.pywt_transform,
mode=self.mode)
return data
def test_wavedecn_coeff_reshape_axes_subset():
# verify round trip is correct when only a subset of axes are transformed:
# wavedecn - >coeffs_to_array-> array_to_coeffs -> waverecn
# This is done for wavedec{1, 2, n}
rng = np.random.RandomState(1234)
mode = 'symmetric'
w = pywt.Wavelet('db2')
N = 16
ndim = 3
for axes in [(-1, ), (0, ), (1, ), (0, 1), (1, 2), (0, 2), None]:
x1 = rng.randn(*([N] * ndim))
coeffs = pywt.wavedecn(x1, w, mode=mode, axes=axes)
coeff_arr, coeff_slices = pywt.coeffs_to_array(coeffs, axes=axes)
if axes is not None:
# if axes is not None, it must be provided to coeffs_to_array
assert_raises(ValueError, pywt.coeffs_to_array, coeffs)
# mismatched axes size
assert_raises(ValueError,
pywt.coeffs_to_array,
coeffs,
axes=(0, 1, 2, 3))
assert_raises(ValueError, pywt.coeffs_to_array, coeffs, axes=())
coeffs2 = pywt.array_to_coeffs(coeff_arr, coeff_slices)
x1r = pywt.waverecn(coeffs2, w, mode=mode, axes=axes)
assert_allclose(x1, x1r, rtol=1e-4, atol=1e-4)
def _transform(self, m, wv = 'db4'):
msyn = np.zeros(mesh.nC)
coeff_map = pywt.wavedecn(msyn.reshape(self.mesh.nCx,self.mesh.nCy,order = 'F'),wv, mode = 'per')
array_map = pywt.coeffs_to_array(coeff_map)
coeff_map = pywt.array_to_coeffs(m.reshape(array_map[0].shape,order= 'F'),array_map[1])
coeff_back_map = pywt.waverecn(coeff_map,wv, mode = 'per')
return Utils.mkvc(coeff_back_map)
def test_wavedecn_coeff_reshape_axes_subset():
# verify round trip is correct when only a subset of axes are transformed:
# wavedecn - >coeffs_to_array-> array_to_coeffs -> waverecn
# This is done for wavedec{1, 2, n}
rng = np.random.RandomState(1234)
mode = 'symmetric'
w = pywt.Wavelet('db2')
N = 16
ndim = 3
for axes in [(-1, ), (0, ), (1, ), (0, 1), (1, 2), (0, 2), None]:
x1 = rng.randn(*([N] * ndim))
coeffs = pywt.wavedecn(x1, w, mode=mode, axes=axes)
coeff_arr, coeff_slices = pywt.coeffs_to_array(coeffs, axes=axes)
if axes is not None:
# if axes is not None, it must be provided to coeffs_to_array
assert_raises(ValueError, pywt.coeffs_to_array, coeffs)
# mismatched axes size
assert_raises(ValueError, pywt.coeffs_to_array, coeffs,
axes=(0, 1, 2, 3))
assert_raises(ValueError, pywt.coeffs_to_array, coeffs,
axes=())
coeffs2 = pywt.array_to_coeffs(coeff_arr, coeff_slices)
x1r = pywt.waverecn(coeffs2, w, mode=mode, axes=axes)
assert_allclose(x1, x1r, rtol=1e-4, atol=1e-4)
def _wavelet_threshold(img, wavelet, threshold=None, sigma=None, mode='soft'):
"""Performs wavelet denoising.
Parameters
----------
img : ndarray (2d or 3d) of ints, uints or floats
Input data to be denoised. `img` can be of any numeric type,
but it is cast into an ndarray of floats for the computation
of the denoised image.
wavelet : string
The type of wavelet to perform. Can be any of the options
pywt.wavelist outputs. For example, this may be any of ``{db1, db2,
db3, db4, haar}``.
sigma : float, optional
The standard deviation of the noise. The noise is estimated when sigma
is None (the default) by the method in [2]_.
threshold : float, optional
The thresholding value. All wavelet coefficients less than this value
are set to 0. The default value (None) uses the SureShrink method found
in [1]_ to remove noise.
mode : {'soft', 'hard'}, optional
An optional argument to choose the type of denoising performed. It
noted that choosing soft thresholding given additive noise finds the
best approximation of the original image.
Returns
-------
out : ndarray
Denoised image.
References
----------
.. [1] Chang, S. Grace, Bin Yu, and Martin Vetterli. "Adaptive wavelet
thresholding for image denoising and compression." Image Processing,
IEEE Transactions on 9.9 (2000): 1532-1546.
DOI: 10.1109/83.862633
.. [2] D. L. Donoho and I. M. Johnstone. "Ideal spatial adaptation
by wavelet shrinkage." Biometrika 81.3 (1994): 425-455.
DOI: 10.1093/biomet/81.3.425
"""
coeffs = pywt.wavedecn(img, wavelet=wavelet)
detail_coeffs = coeffs[-1]['d' * img.ndim]
if sigma is None:
# Estimates via the noise via method in [2]
sigma = np.median(np.abs(detail_coeffs)) / 0.67448975019608171
if threshold is None:
# The BayesShrink threshold from [1]_ in docstring
threshold = sigma**2 / np.sqrt(max(img.var() - sigma**2, 0))
denoised_detail = [{
key: pywt.threshold(level[key], value=threshold, mode=mode)
for key in level
} for level in coeffs[1:]]
denoised_root = pywt.threshold(coeffs[0], value=threshold, mode=mode)
denoised_coeffs = [denoised_root] + [d for d in denoised_detail]
return pywt.waverecn(denoised_coeffs, wavelet)
def test_waverecn():
rstate = np.random.RandomState(1234)
# test 1D through 4D cases
for nd in range(1, 5):
x = rstate.randn(*(4, ) * nd)
coeffs = pywt.wavedecn(x, 'db1')
assert_(len(coeffs) == 3)
assert_allclose(pywt.waverecn(coeffs, 'db1'), x, rtol=tol_double)
def test_waverecn_axes_subsets():
rstate = np.random.RandomState(0)
data = rstate.standard_normal((8, 8, 8, 8))
# test all combinations of 3 out of 4 axes transformed
for axes in combinations((0, 1, 2, 3), 3):
coefs = pywt.wavedecn(data, 'haar', axes=axes)
rec = pywt.waverecn(coefs, 'haar', axes=axes)
assert_allclose(rec, data, atol=1e-14)
def test_waverecn_int_axis():
# waverecn should also work for axes as an integer
rstate = np.random.RandomState(0)
data = rstate.standard_normal((8, 8))
for axis in [0, 1]:
coefs = pywt.wavedecn(data, 'haar', axes=axis)
rec = pywt.waverecn(coefs, 'haar', axes=axis)
assert_allclose(rec, data, atol=1e-14)
def test_waverecn_axes_subsets():
rstate = np.random.RandomState(0)
data = rstate.standard_normal((8, 8, 8, 8))
# test all combinations of 3 out of 4 axes transformed
for axes in combinations((0, 1, 2, 3), 3):
coefs = pywt.wavedecn(data, 'haar', axes=axes)
rec = pywt.waverecn(coefs, 'haar', axes=axes)
assert_allclose(rec, data, atol=1e-14)
def test_waverecn_int_axis():
# waverecn should also work for axes as an integer
rstate = np.random.RandomState(0)
data = rstate.standard_normal((8, 8))
for axis in [0, 1]:
coefs = pywt.wavedecn(data, 'haar', axes=axis)
rec = pywt.waverecn(coefs, 'haar', axes=axis)
assert_allclose(rec, data, atol=1e-14)
def iwtn(data_to_iwt,
wavelet='db4',
mode='per',
dims=None,
dimOpt=None,
dimLenOpt=None):
return pywt.waverecn(mat2wvlt(data_to_iwt, dims, dimOpt, dimLenOpt),
wavelet, mode)
def test_waverecn():
rstate = np.random.RandomState(1234)
# test 1D through 4D cases
for nd in range(1, 5):
x = rstate.randn(*(4, )*nd)
coeffs = pywt.wavedecn(x, 'db1')
assert_(len(coeffs) == 3)
assert_allclose(pywt.waverecn(coeffs, 'db1'), x, rtol=tol_double)
def test_per_axis_wavelets_and_modes():
# tests seperate wavelet and edge mode for each axis.
rstate = np.random.RandomState(1234)
data = rstate.randn(24, 24, 16)
# wavelet can be a string or wavelet object
wavelets = (pywt.Wavelet('haar'), 'sym2', 'db2')
# The default number of levels should be the minimum over this list
max_levels = [
pywt._dwt.dwt_max_level(nd, nf)
for nd, nf in zip(data.shape, wavelets)
]
# mode can be a string or a Modes enum
modes = ('symmetric', 'periodization',
pywt._extensions._pywt.Modes.reflect)
coefs = pywt.wavedecn(data, wavelets, modes)
assert_allclose(pywt.waverecn(coefs, wavelets, modes), data, atol=1e-14)
assert_equal(min(max_levels), len(coefs[1:]))
coefs = pywt.wavedecn(data, wavelets[:1], modes)
assert_allclose(pywt.waverecn(coefs, wavelets[:1], modes),
data,
atol=1e-14)
coefs = pywt.wavedecn(data, wavelets, modes[:1])
assert_allclose(pywt.waverecn(coefs, wavelets, modes[:1]),
data,
atol=1e-14)
# length of wavelets or modes doesn't match the length of axes
assert_raises(ValueError, pywt.wavedecn, data, wavelets[:2])
assert_raises(ValueError, pywt.wavedecn, data, wavelets, mode=modes[:2])
assert_raises(ValueError, pywt.waverecn, coefs, wavelets[:2])
assert_raises(ValueError, pywt.waverecn, coefs, wavelets, mode=modes[:2])
# dwt2/idwt2 also support per-axis wavelets/modes
data2 = data[..., 0]
coefs2 = pywt.wavedec2(data2, wavelets[:2], modes[:2])
assert_allclose(pywt.waverec2(coefs2, wavelets[:2], modes[:2]),
data2,
atol=1e-14)
assert_equal(min(max_levels[:2]), len(coefs2[1:]))
def test_waverecn_all_wavelets_modes():
# test 2D case using all wavelets and modes
rstate = np.random.RandomState(1234)
r = rstate.randn(80, 96)
for wavelet in wavelist:
for mode in pywt.Modes.modes:
coeffs = pywt.wavedecn(r, wavelet, mode=mode)
assert_allclose(pywt.waverecn(coeffs, wavelet, mode=mode),
r, rtol=tol_single, atol=tol_single)
def deriv(self, m, v=None, wv = 'db4'):
if v is not None:
coeff_wv = pywt.wavedecn(v.reshape(self.mesh.nCx,self.mesh.nCy,order = 'F'),wv, mode = 'per')
array_wv = pywt.coeffs_to_array(coeff_wv)
coeff_back = pywt.array_to_coeffs(v,array_wv[1])
coeff_m = pywt.waverecn(coeff_back,wv, mode = 'per')
return Utils.mkvc(coeff_m)
else:
print "not implemented"
def inverse_wavelet_transform(w_coeffs_rgb, coeff_slices, x_shape):
x_hat = np.zeros(x_shape)
for i in range(w_coeffs_rgb.shape[0]):
w_coeffs_list = pywt.array_to_coeffs(w_coeffs_rgb[i, :, :],
coeff_slices)
x_hat[0, :, :, i] = pywt.waverecn(w_coeffs_list,
wavelet='db4',
mode='periodization')
return x_hat
def test_waverecn_all_wavelets_modes():
# test 2D case using all wavelets and modes
rstate = np.random.RandomState(1234)
r = rstate.randn(80, 96)
for wavelet in wavelist:
for mode in pywt.Modes.modes:
coeffs = pywt.wavedecn(r, wavelet, mode=mode)
assert_allclose(pywt.waverecn(coeffs, wavelet, mode=mode),
r, rtol=tol_single, atol=tol_single)
def reconstruct_local_maxima(frames,
fraction_maxima=0.1,
level_max=3,
wavelet='haar'):
print('Decomposing frames ..')
coeffs = pywt.wavedecn(frames, wavelet, level=level_max)
filtered_coeffs = filter_local_maxima(coeffs, fraction_maxima)
print('Reconstructing frames ..')
reconstructed = pywt.waverecn(filtered_coeffs, wavelet)
return reconstructed
def _rmatvec(self, x):
if self.reshape:
x = np.reshape(x, self.dimsd)
x = pywt.array_to_coeffs(x, self.sl, output_format='wavedecn')
y = pywt.waverecn(x,
wavelet=self.waveletadj,
mode='periodization',
axes=(self.dir, ))
y = self.pad.rmatvec(y.ravel())
return y
def test_waverecn_accuracies():
# testing 3D only here
rstate = np.random.RandomState(1234)
x0 = rstate.randn(4, 4, 4)
for dt, tol in dtypes_and_tolerances:
x = x0.astype(dt)
if np.iscomplexobj(x):
x += 1j*rstate.randn(4, 4, 4).astype(x.real.dtype)
coeffs = pywt.wavedecn(x.astype(dt), 'db1')
assert_allclose(pywt.waverecn(coeffs, 'db1'), x, atol=tol, rtol=tol)
def test_waverecn_accuracies():
# testing 3D only here
rstate = np.random.RandomState(1234)
x0 = rstate.randn(4, 4, 4)
for dt, tol in dtypes_and_tolerances:
x = x0.astype(dt)
if np.iscomplexobj(x):
x += 1j * rstate.randn(4, 4, 4).astype(x.real.dtype)
coeffs = pywt.wavedecn(x.astype(dt), 'db1')
assert_allclose(pywt.waverecn(coeffs, 'db1'), x, atol=tol, rtol=tol)
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 calc_wavelet_smooth(line, wavelet_name, level=None):
rep_line = line[::-1] + line[::] + line[::-1] + line[::]
N = len(rep_line)
coeffs = pywt.wavedecn(rep_line, wavelet_name, level=level)
list_, sep_ = pywt.coeffs_to_array(coeffs)
level = level if level is not None else int(np.log2(N))
list_ = [x if j < N / 2**level else 0 for j, x in enumerate(list_)]
coeffs = pywt.array_to_coeffs(list_, sep_)
smooth = pywt.waverecn(coeffs, wavelet_name)
# plt.plot(np.arange(N),smooth,np.arange(N),rep_line);plt.title('name:{}, level:{}'.format(wavelet_name,level));plt.show();
len_line = len(line)
return list(smooth[len_line:len_line * 2])
def test_per_axis_wavelets_and_modes():
# tests seperate wavelet and edge mode for each axis.
rstate = np.random.RandomState(1234)
data = rstate.randn(24, 24, 16)
# wavelet can be a string or wavelet object
wavelets = (pywt.Wavelet('haar'), 'sym2', 'db2')
# The default number of levels should be the minimum over this list
max_levels = [pywt._dwt.dwt_max_level(nd, nf) for nd, nf in
zip(data.shape, wavelets)]
# mode can be a string or a Modes enum
modes = ('symmetric', 'periodization',
pywt._extensions._pywt.Modes.reflect)
coefs = pywt.wavedecn(data, wavelets, modes)
assert_allclose(pywt.waverecn(coefs, wavelets, modes), data, atol=1e-14)
assert_equal(min(max_levels), len(coefs[1:]))
coefs = pywt.wavedecn(data, wavelets[:1], modes)
assert_allclose(pywt.waverecn(coefs, wavelets[:1], modes), data,
atol=1e-14)
coefs = pywt.wavedecn(data, wavelets, modes[:1])
assert_allclose(pywt.waverecn(coefs, wavelets, modes[:1]), data,
atol=1e-14)
# length of wavelets or modes doesn't match the length of axes
assert_raises(ValueError, pywt.wavedecn, data, wavelets[:2])
assert_raises(ValueError, pywt.wavedecn, data, wavelets, mode=modes[:2])
assert_raises(ValueError, pywt.waverecn, coefs, wavelets[:2])
assert_raises(ValueError, pywt.waverecn, coefs, wavelets, mode=modes[:2])
# dwt2/idwt2 also support per-axis wavelets/modes
data2 = data[..., 0]
coefs2 = pywt.wavedec2(data2, wavelets[:2], modes[:2])
assert_allclose(pywt.waverec2(coefs2, wavelets[:2], modes[:2]), data2,
atol=1e-14)
assert_equal(min(max_levels[:2]), len(coefs2[1:]))
def task(dir, name):
X, shape = load_images(dir + name + '/')
arrays = []
coeff_slices = []
for (i, x) in enumerate(X):
coeffs = pywt.wavedec(x, 'db14', level=3)
arr, coeff_slice = pywt.coeffs_to_array(coeffs)
arrays.append(arr)
coeff_slices.append(coeff_slice)
mer = marge(arrays)
coeffs_from_arr = pywt.array_to_coeffs(mer, coeff_slices[0])
cam_recon = pywt.waverecn(coeffs_from_arr, wavelet='db14')
cv2.imwrite('out_' + name + '.jpg', cam_recon.reshape(shape))
def initialize_wl_operators(self):
if self.use_decimated:
H = lambda x: pywt.wavedecn(x, wavelet=self.wl_type, axes=self.axes, level=self.decomp_lvl)
Ht = lambda x: pywt.waverecn(x, wavelet=self.wl_type, axes=self.axes)
else:
if use_swtn:
H = lambda x: pywt.swtn(x, wavelet=self.wl_type, axes=self.axes, level=self.decomp_lvl)
Ht = lambda x: pywt.iswtn(x, wavelet=self.wl_type, axes=self.axes)
else:
H = lambda x: pywt.swt2(np.squeeze(x), wavelet=self.wl_type, axes=self.axes, level=self.decomp_lvl)
# Ht = lambda x : pywt.iswt2(x, wavelet=self.wl_type)
Ht = lambda x: pywt.iswt2(x, wavelet=self.wl_type)[np.newaxis, ...]
return (H, Ht)
def test_multilevel_dtypes_nd():
wavelet = pywt.Wavelet('haar')
for dt_in, dt_out in zip(dtypes_in, dtypes_out):
# wavedecn, waverecn
x = np.ones((8, 8), dtype=dt_in)
errmsg = "wrong dtype returned for {0} input".format(dt_in)
cA, coeffsD2, coeffsD1 = pywt.wavedecn(x, wavelet, level=2)
assert_(cA.dtype == dt_out, "wavedecn: " + errmsg)
for key, c in coeffsD1.items():
assert_(c.dtype == dt_out, "wavedecn: " + errmsg)
for key, c in coeffsD2.items():
assert_(c.dtype == dt_out, "wavedecn: " + errmsg)
x_roundtrip = pywt.waverecn([cA, coeffsD2, coeffsD1], wavelet)
assert_(x_roundtrip.dtype == dt_out, "waverecn: " + errmsg)
def wavelet_denoising(NomDeLImage, Nlevel):
image=su.PullFromSlicer(NomDeLImage)
NumpyImage=sitk.GetArrayFromImage(image)
max_lev = 6 # how many levels of decomposition to draw
coeffs = pywt.wavedecn(NumpyImage, 'db2', mode='zero', level=max_lev) #voir https://pywavelets.readthedocs.io/en/latest/ref/nd-dwt-and-idwt.html#pywt.wavedecn
for i in range(Nlevel-max_lev):
coeffs[(max_lev-i)] = {k: np.zeros_like(v) for k, v in coeffs[(max_lev-i)].items()} #remove highest frequency
coeffs[-(max_lev-i)] = {k: np.zeros_like(v) for k, v in coeffs[-(max_lev-i)].items()} #remove highest frequency
matrice_ondelette=pywt.waverecn(coeffs, 'db2') #mode periodic ou zero
image_ondelette=sitk.GetImageFromArray(matrice_ondelette)
image_ondelette.SetSpacing(image.GetSpacing())
image_ondelette.SetDirection(image.GetDirection())
image_ondelette.SetOrigin(image.GetOrigin())
su.PushToSlicer(image_ondelette,'image_DenoisWave_level0-'+str(Nlevel))
def test_multilevel_dtypes_nd():
wavelet = pywt.Wavelet('haar')
for dt_in, dt_out in zip(dtypes_in, dtypes_out):
# wavedecn, waverecn
x = np.ones((8, 8), dtype=dt_in)
errmsg = "wrong dtype returned for {0} input".format(dt_in)
cA, coeffsD2, coeffsD1 = pywt.wavedecn(x, wavelet, level=2)
assert_(cA.dtype == dt_out, "wavedecn: " + errmsg)
for key, c in coeffsD1.items():
assert_(c.dtype == dt_out, "wavedecn: " + errmsg)
for key, c in coeffsD2.items():
assert_(c.dtype == dt_out, "wavedecn: " + errmsg)
x_roundtrip = pywt.waverecn([cA, coeffsD2, coeffsD1], wavelet)
assert_(x_roundtrip.dtype == dt_out, "waverecn: " + errmsg)
def adj_op(self, x):
if (self.wav == 'dirac'):
return np.reshape(x, self.shape)
if (self.wav == 'fourier'):
return np.fft.ifftn(np.reshape(x, self.shape))
if (self.wav == "dct"):
return scipy.fft.idctn(np.reshape(x, self.shape), norm='ortho')
coeffs_from_arr = pywt.unravel_coeffs(x,
self.coeff_slices,
self.coeff_shapes,
output_format='wavedecn')
return pywt.waverecn(coeffs_from_arr,
wavelet=self.wav,
mode='periodic',
axes=self.axes)
def PrintReconstructions(coeffs, n):
arr, coeff_slices = pywt.coeffs_to_array(coeffs)
#Removing Details
for i in range(n,len(coeff_slices)):
arr[coeff_slices[i]['ad']] = 0
arr[coeff_slices[i]['dd']] = 0
arr[coeff_slices[i]['da']] = 0
D1 = pywt.array_to_coeffs(arr, coeff_slices)
dCat = pywt.waverecn(D1, wavelet)
plt.figure()
plt.title('Reconstructed with level %i of details' %(n-1))
plt.imshow(dCat,cmap=colormap)
return
def test_waverecn_coeff_reshape_odd():
# verify round trip is correct:
# wavedecn - >coeffs_to_array-> array_to_coeffs -> waverecn
rng = np.random.RandomState(1234)
x1 = rng.randn(35, 33)
for mode in pywt.Modes.modes:
for wave in ['haar', ]:
w = pywt.Wavelet(wave)
maxlevel = pywt.dwt_max_level(np.min(x1.shape), w.dec_len)
if maxlevel == 0:
continue
coeffs = pywt.wavedecn(x1, w, mode=mode)
coeff_arr, coeff_slices = pywt.coeffs_to_array(coeffs)
coeffs2 = pywt.array_to_coeffs(coeff_arr, coeff_slices)
x1r = pywt.waverecn(coeffs2, w, mode=mode)
# truncate reconstructed values to original shape
x1r = x1r[[slice(s) for s in x1.shape]]
assert_allclose(x1, x1r, rtol=1e-4, atol=1e-4)
def apply_dwt_filter(y, dwt_type, dwt_level, dwt_thresh_func, dwt_thresh_type):
coeffs = pywt.wavedecn(y, dwt_type, level=dwt_level)
for i in range(1,dwt_level+1):
coeffs[i]["d"] = pywt.threshold(coeffs[i]["d"], thselect(coeffs[i]["d"], dwt_thresh_type), dwt_thresh_func)
return(pywt.waverecn(coeffs, dwt_type))
def time_waverecn(self, D, n, wavelet, dtype):
pywt.waverecn(self.data, wavelet)
def inverse_wavelet_transform(w_coeffs_rgb, coeff_slices, x_shape):
x_hat = np.zeros(x_shape)
for i in range(w_coeffs_rgb.shape[0]):
w_coeffs_list = pywt.array_to_coeffs(w_coeffs_rgb[i,:,:], coeff_slices)
x_hat[0,:,:,i] = pywt.waverecn(w_coeffs_list, wavelet='db4', mode='periodization')
return x_hat
def test_wavedecn_complex():
data = np.ones((4, 4, 4)) + 1j
coeffs = pywt.wavedecn(data, 'db1')
assert_allclose(pywt.waverecn(coeffs, 'db1'), data, rtol=1e-12)
def test_waverecn_lists():
# support coefficient arrays specified as lists instead of arrays
coeffs = [[[1.0]], {'ad': [[0.0]], 'da': [[0.0]], 'dd': [[0.0]]}]
assert_equal(pywt.waverecn(coeffs, 'db1').shape, (2, 2))
def test_waverecn_dtypes():
x = np.ones((4, 4, 4))
for dt, tol in dtypes_and_tolerances:
coeffs = pywt.wavedecn(x.astype(dt), 'db1')
assert_allclose(pywt.waverecn(coeffs, 'db1'), x, atol=tol, rtol=tol)
def _wavelet_threshold(img, wavelet, threshold=None, sigma=None, mode='soft',
wavelet_levels=None):
"""Perform wavelet denoising.
Parameters
----------
img : ndarray (2d or 3d) of ints, uints or floats
Input data to be denoised. `img` can be of any numeric type,
but it is cast into an ndarray of floats for the computation
of the denoised image.
wavelet : string
The type of wavelet to perform. Can be any of the options
pywt.wavelist outputs. For example, this may be any of ``{db1, db2,
db3, db4, haar}``.
sigma : float, optional
The standard deviation of the noise. The noise is estimated when sigma
is None (the default) by the method in [2]_.
threshold : float, optional
The thresholding value. All wavelet coefficients less than this value
are set to 0. The default value (None) uses the BayesShrink method
found in [1]_ to remove noise.
mode : {'soft', 'hard'}, optional
An optional argument to choose the type of denoising performed. It
noted that choosing soft thresholding given additive noise finds the
best approximation of the original image.
wavelet_levels : int or None, optional
The number of wavelet decomposition levels to use. The default is
three less than the maximum number of possible decomposition levels
(see Notes below).
Returns
-------
out : ndarray
Denoised image.
Notes
-----
Reference [1]_ used four levels of wavelet decomposition. To be more
flexible for a range of input sizes, the implementation here stops 3 levels
prior to the maximum level of decomposition for `img` (the exact # of
levels thus depends on `img.shape` and the chosen wavelet). BayesShrink
variance estimation doesn't work well on levels with extremely small
coefficient arrays. This is the rationale for skipping a few of the
coarsest levels. The user can override the automated setting by explicitly
specifying `wavelet_levels`.
References
----------
.. [1] Chang, S. Grace, Bin Yu, and Martin Vetterli. "Adaptive wavelet
thresholding for image denoising and compression." Image Processing,
IEEE Transactions on 9.9 (2000): 1532-1546.
DOI: 10.1109/83.862633
.. [2] D. L. Donoho and I. M. Johnstone. "Ideal spatial adaptation
by wavelet shrinkage." Biometrika 81.3 (1994): 425-455.
DOI: 10.1093/biomet/81.3.425
"""
wavelet = pywt.Wavelet(wavelet)
# Determine the number of wavelet decomposition levels
if wavelet_levels is None:
# Determine the maximum number of possible levels for img
dlen = wavelet.dec_len
wavelet_levels = np.min(
[pywt.dwt_max_level(s, dlen) for s in img.shape])
# Skip coarsest wavelet scales (see Notes in docstring).
wavelet_levels = max(wavelet_levels - 3, 1)
coeffs = pywt.wavedecn(img, wavelet=wavelet, level=wavelet_levels)
# Detail coefficients at each decomposition level
dcoeffs = coeffs[1:]
if sigma is None:
# Estimate the noise via the method in [2]_
detail_coeffs = dcoeffs[-1]['d' * img.ndim]
sigma = _sigma_est_dwt(detail_coeffs, distribution='Gaussian')
if threshold is None:
# The BayesShrink thresholds from [1]_ in docstring
var = sigma**2
threshold = [{key: _bayes_thresh(level[key], var) for key in level}
for level in dcoeffs]
if np.isscalar(threshold):
# A single threshold for all coefficient arrays
denoised_detail = [{key: pywt.threshold(level[key],
value=threshold,
mode=mode) for key in level}
for level in dcoeffs]
else:
# Dict of unique threshold coefficients for each detail coeff. array
denoised_detail = [{key: pywt.threshold(level[key],
value=thresh[key],
mode=mode) for key in level}
for thresh, level in zip(threshold, dcoeffs)]
denoised_coeffs = [coeffs[0]] + denoised_detail
return pywt.waverecn(denoised_coeffs, wavelet)
def iwtn(data_to_iwt, wavelet='db4', mode='per', dims=None, dimOpt=None, dimLenOpt=None):
return pywt.waverecn(mat2wvlt(data_to_iwt, dims, dimOpt, dimLenOpt), wavelet, mode)
def _wavelet_threshold(image, wavelet, method=None, threshold=None,
sigma=None, mode='soft', wavelet_levels=None):
"""Perform wavelet thresholding.
Parameters
----------
image : ndarray (2d or 3d) of ints, uints or floats
Input data to be denoised. `image` can be of any numeric type,
but it is cast into an ndarray of floats for the computation
of the denoised image.
wavelet : string
The type of wavelet to perform. Can be any of the options
pywt.wavelist outputs. For example, this may be any of ``{db1, db2,
db3, db4, haar}``.
method : {'BayesShrink', 'VisuShrink'}, optional
Thresholding method to be used. The currently supported methods are
"BayesShrink" [1]_ and "VisuShrink" [2]_. If it is set to None, a
user-specified ``threshold`` must be supplied instead.
threshold : float, optional
The thresholding value to apply during wavelet coefficient
thresholding. The default value (None) uses the selected ``method`` to
estimate appropriate threshold(s) for noise removal.
sigma : float, optional
The standard deviation of the noise. The noise is estimated when sigma
is None (the default) by the method in [2]_.
mode : {'soft', 'hard'}, optional
An optional argument to choose the type of denoising performed. It
noted that choosing soft thresholding given additive noise finds the
best approximation of the original image.
wavelet_levels : int or None, optional
The number of wavelet decomposition levels to use. The default is
three less than the maximum number of possible decomposition levels
(see Notes below).
Returns
-------
out : ndarray
Denoised image.
References
----------
.. [1] Chang, S. Grace, Bin Yu, and Martin Vetterli. "Adaptive wavelet
thresholding for image denoising and compression." Image Processing,
IEEE Transactions on 9.9 (2000): 1532-1546.
:DOI:`10.1109/83.862633`
.. [2] D. L. Donoho and I. M. Johnstone. "Ideal spatial adaptation
by wavelet shrinkage." Biometrika 81.3 (1994): 425-455.
:DOI:`10.1093/biomet/81.3.425`
"""
wavelet = pywt.Wavelet(wavelet)
if not wavelet.orthogonal:
warn(("Wavelet thresholding was designed for use with orthogonal "
"wavelets. For nonorthogonal wavelets such as {}, results are "
"likely to be suboptimal.").format(wavelet.name))
# original_extent is used to workaround PyWavelets issue #80
# odd-sized input results in an image with 1 extra sample after waverecn
original_extent = tuple(slice(s) for s in image.shape)
# Determine the number of wavelet decomposition levels
if wavelet_levels is None:
# Determine the maximum number of possible levels for image
dlen = wavelet.dec_len
wavelet_levels = np.min(
[pywt.dwt_max_level(s, dlen) for s in image.shape])
# Skip coarsest wavelet scales (see Notes in docstring).
wavelet_levels = max(wavelet_levels - 3, 1)
coeffs = pywt.wavedecn(image, wavelet=wavelet, level=wavelet_levels)
# Detail coefficients at each decomposition level
dcoeffs = coeffs[1:]
if sigma is None:
# Estimate the noise via the method in [2]_
detail_coeffs = dcoeffs[-1]['d' * image.ndim]
sigma = _sigma_est_dwt(detail_coeffs, distribution='Gaussian')
if method is not None and threshold is not None:
warn(("Thresholding method {} selected. The user-specified threshold "
"will be ignored.").format(method))
if threshold is None:
var = sigma**2
if method is None:
raise ValueError(
"If method is None, a threshold must be provided.")
elif method == "BayesShrink":
# The BayesShrink thresholds from [1]_ in docstring
threshold = [{key: _bayes_thresh(level[key], var) for key in level}
for level in dcoeffs]
elif method == "VisuShrink":
# The VisuShrink thresholds from [2]_ in docstring
threshold = _universal_thresh(image, sigma)
else:
raise ValueError("Unrecognized method: {}".format(method))
if np.isscalar(threshold):
# A single threshold for all coefficient arrays
denoised_detail = [{key: pywt.threshold(level[key],
value=threshold,
mode=mode) for key in level}
for level in dcoeffs]
else:
# Dict of unique threshold coefficients for each detail coeff. array
denoised_detail = [{key: pywt.threshold(level[key],
value=thresh[key],
mode=mode) for key in level}
for thresh, level in zip(threshold, dcoeffs)]
denoised_coeffs = [coeffs[0]] + denoised_detail
return pywt.waverecn(denoised_coeffs, wavelet)[original_extent]