def remove_zinger(tomo, dif, size=3, ncore=None, nchunk=None):
"""
Remove high intensity bright spots from 3D tomographic data.
Parameters
----------
tomo : ndarray
3D tomographic data.
dif : float
Expected difference value between outlier measurement and
the median filtered raw measurement.
size : int, optional
Size of the median filter.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Corrected 3D tomographic data.
"""
arr = mp.distribute_jobs(tomo,
func=_remove_zinger,
args=(dif, size),
axis=0,
ncore=ncore,
nchunk=nchunk)
return arr
def remove_stripe2(tomo, nblock=0, alpha=1.5, ncore=None, nchunk=None):
"""
Remove horizontal stripes from sinogram using Titarenko's
approach :cite:`Miqueles:14`.
Parameters
----------
tomo : ndarray
3D tomographic data.
nblock : int, optional
Number of blocks.
alpha : int, optional
Damping factor.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Corrected 3D tomographic data.
"""
arr = mp.distribute_jobs(tomo,
func=_remove_stripe2,
args=(nblock, alpha),
axis=1,
ncore=ncore,
nchunk=nchunk)
return arr
def median_filter(arr, size=3, axis=0, ncore=None, nchunk=None):
"""
Apply median filter to 3D array along specified axis.
Parameters
----------
arr : ndarray
Arbitrary 3D array.
size : int, optional
The size of the filter.
axis : int, optional
Axis along which median filtering is performed.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Median filtered 3D array.
"""
arr = as_float32(arr)
arr = mp.distribute_jobs(
arr,
func=_median_filter,
args=(size, axis),
axis=axis,
ncore=ncore,
nchunk=nchunk)
return arr
def correct_air(tomo, air=10, ncore=None, nchunk=None):
"""
Weight sinogram such that the left and right image boundaries
(i.e., typically the air region around the object) are set to one
and all intermediate values are scaled linearly.
Parameters
----------
tomo : ndarray
3D tomographic data.
air : int, optional
Number of pixels at each boundary to calculate the scaling factor.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Corrected 3D tomographic data.
"""
tomo = as_float32(tomo)
air = as_int32(air)
arr = mp.distribute_jobs(tomo,
func=_correct_air,
args=(air, ),
axis=0,
ncore=ncore,
nchunk=nchunk)
return arr
def retrieve_phase(
tomo, psize=1e-4, dist=50, energy=20,
alpha=1e-4, pad=True, ind=None):
"""
Perform single-step phase retrieval from phase-contrast measurements
:cite:`Paganin:02`.
Parameters
----------
tomo : ndarray
3D tomographic data.
psize : float, optional
Detector pixel size in cm.
dist : float, optional
Propagation distance of the wavefront in cm.
energy : float, optional
Energy of incident wave in keV.
alpha : float, optional
Regularization parameter.
pad : bool, optional
If True, extend the size of the projections by padding with zeros.
ind : array of int, optional
Projection indices at which the phase retrieval is applied.
Returns
-------
ndarray
Approximated 3D tomographic phase data.
"""
if type(tomo) == str and tomo == 'SHARED':
tomo = mp.shared_data
else:
arr = mp.distribute_jobs(
tomo, func=retrieve_phase,
args=(psize, dist, energy, alpha, pad), axis=0)
return arr
dx, dy, dz = tomo.shape
if ind is None:
ind = np.arange(0, dx)
# Compute the filter.
H, xshift, yshift, prj = _paganin_filter(
tomo, psize, dist, energy, alpha, pad)
for m in ind:
proj = tomo[m, :, :]
if pad:
prj[xshift:dy + xshift, yshift:dz + yshift] = proj
fproj = np.fft.fft2(prj)
filtproj = np.multiply(H, fproj)
tmp = np.real(np.fft.ifft2(filtproj)) / np.max(H)
proj = tmp[xshift:dy + xshift, yshift:dz + yshift]
elif not pad:
fproj = np.fft.fft2(proj)
filtproj = np.multiply(H, fproj)
proj = np.real(np.fft.ifft2(filtproj)) / np.max(H)
tomo[m, :, :] = proj
def median_filter(tomo, size=3, axis=0, ind=None):
"""
Apply median filter to a 3D array along a specified axis.
Parameters
----------
tomo : ndarray
Arbitrary 3D array.
size : int, optional
The size of the filter.
axis : int, optional
Axis along which median filtering is performed.
ind : array of int, optional
Indices at which the filtering is applied.
Returns
-------
ndarray
Median filtered 3D array.
"""
if type(tomo) == str and tomo == 'SHARED':
tomo = mp.shared_data
else:
arr = mp.distribute_jobs(
tomo, func=median_filter, axis=axis,
args=(size, axis))
return arr
dx, dy, dz = tomo.shape
if ind is None:
if axis == 0:
ind = np.arange(0, dx)
elif axis == 1:
ind = np.arange(0, dy)
elif axis == 2:
ind = np.arange(0, dz)
if axis == 0:
for m in ind:
tomo[m, :, :] = filters.median_filter(
tomo[m, :, :], (size, size))
elif axis == 1:
for m in ind:
tomo[:, m, :] = filters.median_filter(
tomo[:, m, :], (size, size))
elif axis == 2:
for m in ind:
tomo[:, :, m] = filters.median_filter(
tomo[:, :, m], (size, size))
def normalize(tomo, flat, dark, cutoff=None, ind=None):
"""
Normalize raw projection data using the flat and dark field projections.
Parameters
----------
tomo : ndarray
3D tomographic data.
flat : ndarray
3D flat field data.
dark : ndarray
3D dark field data.
cutoff : float, optional
Permitted maximum vaue for the normalized data.
ind : array of int, optional
Projection indices at which the normalization is applied.
Returns
-------
ndarray
Normalized 3D tomographic data.
"""
if type(tomo) == str and tomo == 'SHARED':
tomo = mp.shared_data
else:
arr = mp.distribute_jobs(
tomo, func=normalize, axis=0,
args=(flat, dark, cutoff))
return arr
dx, dy, dz = tomo.shape
if ind is None:
ind = np.arange(0, dx)
# Calculate average flat and dark fields for normalization.
flat = flat.mean(axis=0)
dark = dark.mean(axis=0)
# Avoid zero division in normalization
denom = flat - dark
denom[denom == 0] = 1e-6
for m in ind:
proj = tomo[m, :, :]
proj = np.divide(proj - dark, denom)
if cutoff is not None:
proj[proj > cutoff] = cutoff
tomo[m, :, :] = proj
def retrieve_phase(tomo,
psize=1e-4,
dist=50,
energy=20,
alpha=1e-3,
pad=True,
ncore=None,
nchunk=None):
"""
Perform single-step phase retrieval from phase-contrast measurements
:cite:`Paganin:02`.
Parameters
----------
tomo : ndarray
3D tomographic data.
psize : float, optional
Detector pixel size in cm.
dist : float, optional
Propagation distance of the wavefront in cm.
energy : float, optional
Energy of incident wave in keV.
alpha : float, optional
Regularization parameter.
pad : bool, optional
If True, extend the size of the projections by padding with zeros.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Approximated 3D tomographic phase data.
"""
# Compute the filter.
H, xshift, yshift, prj = _paganin_filter(tomo, psize, dist, energy, alpha,
pad)
arr = mp.distribute_jobs(tomo,
func=_retrieve_phase,
args=(H, xshift, yshift, prj, pad),
axis=0,
ncore=ncore,
nchunk=nchunk)
return arr
def project(obj, theta, center=None, ncore=None, nchunk=None):
"""
Project x-rays through a given 3D object.
Parameters
----------
obj : ndarray
Voxelized 3D object.
theta : array
Projection angles in radian.
center: array, optional
Location of rotation axis.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
3D tomographic data.
"""
obj = as_float32(obj)
# Estimate data dimensions.
ox, oy, oz = obj.shape
dx = len(theta)
dy = ox
dz = np.ceil(np.sqrt(oy * oy + oz * oz)).astype('int')
tomo = np.zeros((dx, dy, dz), dtype='float32')
if center is None:
center = np.ones(dy, dtype='float32') * dz / 2.
elif np.array(center).size == 1:
center = np.ones(dy, dtype='float32') * center
theta = as_float32(theta)
center = as_float32(center)
_init_shared(obj)
arr = mp.distribute_jobs(tomo,
func=_project,
args=(theta, center),
axis=0,
ncore=ncore,
nchunk=nchunk)
return arr
def remove_stripe1(tomo,
level=None,
wname='db5',
sigma=2,
pad=True,
ncore=None,
nchunk=None):
"""
Remove horizontal stripes from sinogram using the Fourier-Wavelet (FW)
based method :cite:`Munch:09`.
Parameters
----------
tomo : ndarray
3D tomographic data.
level : int, optional
Number of discrete wavelet transform levels.
wname : str, optional
Type of the wavelet filter. 'haar', 'db5', sym5', etc.
sigma : float, optional
Damping parameter in Fourier space.
pad : bool, optional
If True, extend the size of the sinogram by padding with zeros.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Corrected 3D tomographic data.
"""
if level is None:
size = np.max(tomo.shape)
level = int(np.ceil(np.log2(size)))
arr = mp.distribute_jobs(tomo,
func=_remove_stripe1,
args=(level, wname, sigma, pad),
axis=1,
ncore=ncore,
nchunk=nchunk)
return arr
def gaussian_filter(arr, sigma, order=0, axis=0, ncore=None, nchunk=None):
"""
Apply Gaussian filter to 3D array along specified axis.
Parameters
----------
arr : ndarray
Arbitrary 3D array.
sigma : scalar or sequence of scalars
Standard deviation for Gaussian kernel. The standard deviations
of the Gaussian filter are given for each axis as a sequence, or
as a single number, in which case it is equal for all axes.
order : {0, 1, 2, 3} or sequence from same set, optional
Order of the filter along each axis is given as a sequence
of integers, or as a single number. An order of 0 corresponds
to convolution with a Gaussian kernel. An order of 1, 2, or 3
corresponds to convolution with the first, second or third
derivatives of a Gaussian. Higher order derivatives are not
implemented
axis : int, optional
Axis along which median filtering is performed.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
3D array of same shape as input.
"""
arr = as_float32(arr)
arr = mp.distribute_jobs(
arr,
func=_gaussian_filter,
args=(sigma, order, axis),
axis=axis,
ncore=ncore,
nchunk=nchunk)
return arr
def remove_zinger(tomo, dif=1000, size=3, ind=None):
"""
Remove high intensity bright spots from tomographic data.
Parameters
----------
tomo : ndarray
3D tomographic data.
dif : float, optional
Expected difference value between outlier measurements and
the median filtered raw measurements.
size : int, optional
Size of the median filter.
ind : array of int, optional
Projection indices at which the zinger removal is applied.
Returns
-------
ndarray
Corrected 3D tomographic data.
"""
if type(tomo) == str and tomo == 'SHARED':
tomo = mp.shared_data
else:
arr = mp.distribute_jobs(
tomo, func=remove_zinger, axis=0,
args=(dif, size))
return arr
dx, dy, dz = tomo.shape
if ind is None:
ind = np.arange(0, dx)
mask = np.zeros((1, dy, dz))
for m in ind:
tmp = filters.median_filter(tomo[m, :, :], (size, size))
mask = ((tomo[m, :, :] - tmp) >= dif).astype(int)
tomo[m, :, :] = tmp * mask + tomo[m, :, :] * (1 - mask)
def normalize(tomo, flat, dark, cutoff=None, ncore=None, nchunk=None):
"""
Normalize raw projection data using the flat and dark field projections.
Parameters
----------
tomo : ndarray
3D tomographic data.
flat : ndarray
3D flat field data.
dark : ndarray
3D dark field data.
cutoff : float, optional
Permitted maximum vaue for the normalized data.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Normalized 3D tomographic data.
"""
tomo = as_float32(tomo)
flat = as_float32(flat)
dark = as_float32(dark)
# Calculate average flat and dark fields for normalization.
flat = flat.mean(axis=0)
dark = dark.mean(axis=0)
arr = mp.distribute_jobs(tomo,
func=_normalize,
args=(flat, dark, cutoff),
axis=0,
ncore=ncore,
nchunk=nchunk)
return arr
def pml_hybrid(tomo,
theta,
center=None,
emission=True,
recon=None,
num_gridx=None,
num_gridy=None,
num_iter=1,
reg_par=None,
ncore=None,
nchunk=None):
"""
Reconstruct object from projection data using penalized maximum
likelihood algorithm with weighted linear and quadratic penalties
:cite:`Chang:04`.
Parameters
----------
tomo : ndarray
3D tomographic data.
theta : array
Projection angles in radian.
center: array, optional
Location of rotation axis.
emission : bool, optional
Determines whether data is emission or transmission type.
recon : ndarray, optional
Initial values of the reconstruction object.
num_gridx, num_gridy : int, optional
Number of pixels along x- and y-axes in the reconstruction grid.
num_iter : int, optional
Number of algorithm iterations performed.
reg_par : list, optional
Regularization hyperparameters as an array, (beta, delta).
num_block : int, optional
Number of data blocks for intermediate updating the object.
ind_block : array of int, optional
Order of projections to be used for updating.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Reconstructed 3D object.
"""
tomo = as_float32(tomo)
theta = as_float32(theta)
dx, dy, dz = tomo.shape
if center is None:
center = np.ones(dy, dtype='float32') * dz / 2.
elif np.array(center).size == 1:
center = np.ones(dy, dtype='float32') * center
if num_gridx is None:
num_gridx = dz
if num_gridy is None:
num_gridy = dz
if emission is False:
tomo = -np.log(tomo)
if recon is None:
recon = 1e-6 * np.ones((dy, num_gridx, num_gridy), dtype='float32')
if reg_par is None:
reg_par = np.ones(10, dtype="float32")
center = as_float32(center)
recon = as_float32(recon)
num_gridx = as_int32(num_gridx)
num_gridy = as_int32(num_gridy)
num_iter = as_int32(num_iter)
reg_par = as_float32(reg_par)
_init_shared(tomo)
arr = mp.distribute_jobs(recon,
func=_pml_hybrid,
args=(theta, center, num_gridx, num_gridy,
num_iter, reg_par),
axis=0,
ncore=ncore,
nchunk=nchunk)
return arr
def art(tomo,
theta,
center=None,
emission=True,
recon=None,
num_gridx=None,
num_gridy=None,
num_iter=1,
ncore=None,
nchunk=None):
"""
Reconstruct object from projection data using algebraic reconstruction
technique (ART) :cite:`Kak:98`.
Parameters
----------
tomo : ndarray
3D tomographic data.
theta : array
Projection angles in radian.
center: array, optional
Location of rotation axis.
emission : bool, optional
Determines whether data is emission or transmission type.
recon : ndarray, optional
Initial values of the reconstruction object.
num_gridx, num_gridy : int, optional
Number of pixels along x- and y-axes in the reconstruction grid.
num_iter : int, optional
Number of algorithm iterations performed.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Reconstructed 3D object.
"""
tomo = as_float32(tomo)
theta = as_float32(theta)
dx, dy, dz = tomo.shape
if center is None:
center = np.ones(dy, dtype='float32') * dz / 2.
elif np.array(center).size == 1:
center = np.ones(dy, dtype='float32') * center
if num_gridx is None:
num_gridx = dz
if num_gridy is None:
num_gridy = dz
if emission is False:
tomo = -np.log(tomo)
if recon is None:
recon = 1e-6 * np.ones((dy, num_gridx, num_gridy), dtype='float32')
center = as_float32(center)
recon = as_float32(recon)
num_gridx = as_int32(num_gridx)
num_gridy = as_int32(num_gridy)
num_iter = as_int32(num_iter)
_init_shared(tomo)
arr = mp.distribute_jobs(recon,
func=_art,
args=(theta, center, num_gridx, num_gridy,
num_iter),
axis=0,
ncore=ncore,
nchunk=nchunk)
return arr
def osem(tomo,
theta,
center=None,
emission=True,
recon=None,
num_gridx=None,
num_gridy=None,
num_iter=1,
num_block=1,
ind_block=None,
ncore=None,
nchunk=None):
"""
Reconstruct object from projection data using ordered-subset
expectation-maximization (OS-EM) :cite:`Hudson:94`.
Parameters
----------
tomo : ndarray
3D tomographic data.
theta : array
Projection angles in radian.
center: array, optional
Location of rotation axis.
emission : bool, optional
Determines whether data is emission or transmission type.
recon : ndarray, optional
Initial values of the reconstruction object.
num_gridx, num_gridy : int, optional
Number of pixels along x- and y-axes in the reconstruction grid.
num_iter : int, optional
Number of algorithm iterations performed.
num_block : int, optional
Number of data blocks for intermediate updating the object.
ind_block : array of int, optional
Order of projections to be used for updating.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Reconstructed 3D object.
"""
tomo = as_float32(tomo)
theta = as_float32(theta)
dx, dy, dz = tomo.shape
if center is None:
center = np.ones(dy, dtype='float32') * dz / 2.
elif np.array(center).size == 1:
center = np.ones(dy, dtype='float32') * center
if num_gridx is None:
num_gridx = dz
if num_gridy is None:
num_gridy = dz
if emission is False:
tomo = -np.log(tomo)
if recon is None:
recon = 1e-6 * np.ones((dy, num_gridx, num_gridy), dtype='float32')
if ind_block is None:
ind_block = np.arange(0, dx).astype("float32")
center = as_float32(center)
recon = as_float32(recon)
num_gridx = as_int32(num_gridx)
num_gridy = as_int32(num_gridy)
num_iter = as_int32(num_iter)
num_block = as_int32(num_block)
ind_block = as_float32(ind_block)
_init_shared(tomo)
arr = mp.distribute_jobs(recon,
func=_osem,
args=(theta, center, num_gridx, num_gridy,
num_iter, num_block, ind_block),
axis=0,
ncore=ncore,
nchunk=nchunk)
return arr
def gridrec(tomo,
theta,
center=None,
emission=True,
num_gridx=None,
num_gridy=None,
filter_name='shepp',
ncore=None,
nchunk=None):
"""
Reconstruct object from projection data using gridrec algorithm
:cite:`Dowd:99`.
Parameters
----------
tomo : ndarray
3D tomographic data.
theta : array
Projection angles in radian.
center: array, optional
Location of rotation axis.
emission : bool, optional
Determines whether data is emission or transmission type.
num_gridx, num_gridy : int, optional
Number of pixels along x- and y-axes in the reconstruction grid.
filter_name : str, optional
Filter name for weighting. 'shepp', 'hann', 'hamming', 'ramlak',
'cosine' or 'none'.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Reconstructed 3D object.
"""
tomo = as_float32(tomo)
theta = as_float32(theta)
dx, dy, dz = tomo.shape
# Gridrec accepts even number of slices.
is_odd = False
if tomo.shape[1] % 2 != 0:
is_odd = True
lasttomo = np.expand_dims(tomo[:, -1, :], 1)
tomo = np.append(tomo, lasttomo, 1)
dy += 1
if center is None:
center = np.ones(dy, dtype='float32') * dz / 2.
elif np.array(center).size == 1:
center = np.ones(dy, dtype='float32') * center
if num_gridx is None:
num_gridx = dz
if num_gridy is None:
num_gridy = dz
if emission is False:
tomo = -np.log(tomo)
recon = 1e-6 * np.ones((dy, num_gridx, num_gridy), dtype='float32')
filter_name = np.array(filter_name, dtype=(str, 16))
center = as_float32(center)
num_gridx = as_int32(num_gridx)
num_gridy = as_int32(num_gridy)
# Chunk size can't be smaller than two for gridrec.
if ncore is None:
ncore = multiprocessing.cpu_count()
if dx < ncore:
ncore = dx
if nchunk is None:
nchunk = (dy - 1) // ncore + 1
if nchunk < 2:
nchunk = 2
_init_shared(tomo)
arr = mp.distribute_jobs(recon,
func=_gridrec,
args=(theta, center, num_gridx, num_gridy,
filter_name),
axis=0,
ncore=ncore,
nchunk=nchunk)
# Dump last slice if original number of sice was even.
if is_odd:
arr = arr[0:-1, :, :]
return arr
def fbp(tomo,
theta,
center=None,
emission=True,
num_gridx=None,
num_gridy=None,
filter_name='shepp',
ncore=None,
nchunk=None):
"""
Reconstruct object from projection data using filtered back
projection (FBP).
Warning
-------
Filter not implemented yet.
Parameters
----------
tomo : ndarray
3D tomographic data.
theta : array
Projection angles in radian.
center: array, optional
Location of rotation axis.
emission : bool, optional
Determines whether data is emission or transmission type.
num_gridx, num_gridy : int, optional
Number of pixels along x- and y-axes in the reconstruction grid.
filter_name : str, optional
Filter name for weighting. 'shepp', 'hann', 'hamming', 'ramlak',
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Reconstructed 3D object.
"""
tomo = as_float32(tomo)
theta = as_float32(theta)
dx, dy, dz = tomo.shape
if center is None:
center = np.ones(dy, dtype='float32') * dz / 2.
elif np.array(center).size == 1:
center = np.ones(dy, dtype='float32') * center
if num_gridx is None:
num_gridx = dz
if num_gridy is None:
num_gridy = dz
if emission is False:
tomo = -np.log(tomo)
recon = 1e-6 * np.ones((dy, num_gridx, num_gridy), dtype='float32')
filter_name = np.array(filter_name, dtype=(str, 16))
center = as_float32(center)
num_gridx = as_int32(num_gridx)
num_gridy = as_int32(num_gridy)
_init_shared(tomo)
arr = mp.distribute_jobs(recon,
func=_fbp,
args=(theta, center, num_gridx, num_gridy,
filter_name),
axis=0,
ncore=ncore,
nchunk=nchunk)
return arr
def remove_stripe(
tomo, level=None, wname='db5',
sigma=2, pad=True, ind=None):
"""
Remove horizontal stripes from sinogram using the Fourier-Wavelet (FW)
based method :cite:`Munch:09`.
Parameters
----------
tomo : ndarray
3D tomographic data.
level : int, optional
Number of discrete wavelet transform levels.
wname : str, optional
Type of the wavelet filter. 'haar', 'db5', sym5', etc.
sigma : float, optional
Damping parameter in Fourier space.
pad : bool, optional
If True, extend the size of the sinogram by padding with zeros.
ind : array of int, optional
Sinogram indices at which the stripe removal is applied.
Returns
-------
ndarray
Corrected 3D tomographic data.
"""
if type(tomo) == str and tomo == 'SHARED':
tomo = mp.shared_data
else:
arr = mp.distribute_jobs(
tomo, func=remove_stripe, axis=1,
args=(level, wname, sigma, pad))
return arr
dx, dy, dz = tomo.shape
if ind is None:
ind = np.arange(0, dy)
if level is None:
size = np.max(tomo.shape)
level = int(np.ceil(np.log2(size)))
# pad temp image.
nx = dx
if pad:
nx = dx + dx / 8
xshift = int((nx - dx) / 2.)
sli = np.zeros((nx, dz), dtype='float32')
for n in ind:
sli[xshift:dx + xshift, :] = tomo[:, n, :]
# Wavelet decomposition.
cH = []
cV = []
cD = []
for m in range(level):
sli, (cHt, cVt, cDt) = pywt.dwt2(sli, wname)
cH.append(cHt)
cV.append(cVt)
cD.append(cDt)
# FFT transform of horizontal frequency bands.
for m in range(level):
# FFT
fcV = np.fft.fftshift(np.fft.fft(cV[m], axis=0))
my, mx = fcV.shape
# Damping of ring artifact information.
y_hat = (np.arange(-my, my, 2, dtype='float') + 1) / 2
damp = 1 - np.exp(-np.power(y_hat, 2) / (2 * np.power(sigma, 2)))
fcV = np.multiply(fcV, np.transpose(np.tile(damp, (mx, 1))))
# Inverse FFT.
cV[m] = np.real(np.fft.ifft(np.fft.ifftshift(fcV), axis=0))
# Wavelet reconstruction.
for m in range(level)[::-1]:
sli = sli[0:cH[m].shape[0], 0:cH[m].shape[1]]
sli = pywt.idwt2((sli, (cH[m], cV[m], cD[m])), wname)
tomo[:, n, :] = sli[xshift:dx + xshift, 0:dz]