def write_center(tomo,
theta,
dpath='tmp/center',
cen_range=None,
ind=None,
mask=False,
ratio=1.,
sinogram_order=False,
algorithm='gridrec',
filter_name='parzen'):
"""
Save images reconstructed with a range of rotation centers.
Helps finding the rotation center manually by visual inspection of
images reconstructed with a set of different centers.The output
images are put into a specified folder and are named by the
center position corresponding to the image.
Parameters
----------
tomo : ndarray
3D tomographic data.
theta : array
Projection angles in radian.
dpath : str, optional
Folder name to save output images.
cen_range : list, optional
[start, end, step] Range of center values.
ind : int, optional
Index of the slice to be used for reconstruction.
mask : bool, optional
If ``True``, apply a circular mask to the reconstructed image to
limit the analysis into a circular region.
ratio : float, optional
The ratio of the radius of the circular mask to the edge of the
reconstructed image.
sinogram_order: bool, optional
Determins whether data is a stack of sinograms (True, y-axis first axis)
or a stack of radiographs (False, theta first axis).
algorithm : {str, function}
One of the following string values.
'art'
Algebraic reconstruction technique :cite:`Kak:98`.
'bart'
Block algebraic reconstruction technique.
'fbp'
Filtered back-projection algorithm.
'gridrec'
Fourier grid reconstruction algorithm :cite:`Dowd:99`,
:cite:`Rivers:06`.
'mlem'
Maximum-likelihood expectation maximization algorithm
:cite:`Dempster:77`.
'osem'
Ordered-subset expectation maximization algorithm
:cite:`Hudson:94`.
'ospml_hybrid'
Ordered-subset penalized maximum likelihood algorithm with
weighted linear and quadratic penalties.
'ospml_quad'
Ordered-subset penalized maximum likelihood algorithm with
quadratic penalties.
'pml_hybrid'
Penalized maximum likelihood algorithm with weighted linear
and quadratic penalties :cite:`Chang:04`.
'pml_quad'
Penalized maximum likelihood algorithm with quadratic penalty.
'sirt'
Simultaneous algebraic reconstruction technique.
'tv'
Total Variation reconstruction technique
:cite:`Chambolle:11`.
'grad'
Gradient descent method with a constant step size
filter_name : str, optional
Name of the filter for analytic reconstruction.
'none'
No filter.
'shepp'
Shepp-Logan filter (default).
'cosine'
Cosine filter.
'hann'
Cosine filter.
'hamming'
Hamming filter.
'ramlak'
Ram-Lak filter.
'parzen'
Parzen filter.
'butterworth'
Butterworth filter.
'custom'
A numpy array of size `next_power_of_2(num_detector_columns)/2`
specifying a custom filter in Fourier domain. The first element
of the filter should be the zero-frequency component.
'custom2d'
A numpy array of size `num_projections*next_power_of_2(num_detector_columns)/2`
specifying a custom angle-dependent filter in Fourier domain. The first element
of each filter should be the zero-frequency component.
"""
tomo = dtype.as_float32(tomo)
theta = dtype.as_float32(theta)
if sinogram_order:
dy, dt, dx = tomo.shape
else:
dt, dy, dx = tomo.shape
if ind is None:
ind = dy // 2
if cen_range is None:
center = np.arange(dx / 2 - 5, dx / 2 + 5, 0.5)
else:
center = np.arange(*cen_range)
stack = dtype.empty_shared_array((len(center), dt, dx))
for m in range(center.size):
if sinogram_order:
stack[m] = tomo[ind]
else:
stack[m] = tomo[:, ind, :]
# Reconstruct the same slice with a range of centers.
rec = recon(stack,
theta,
center=center,
sinogram_order=True,
algorithm=algorithm,
filter_name=filter_name,
nchunk=1)
# Apply circular mask.
if mask is True:
rec = circ_mask(rec, axis=0)
# Save images to a temporary folder.
for m in range(len(center)):
write_tiff(data=rec[m], fname=dpath, digit='{0:.2f}'.format(center[m]))
def align_seq(
prj, ang, fdir='.', iters=10, pad=(0, 0),
blur=True, center=None, algorithm='sirt',
upsample_factor=10, rin=0.5, rout=0.8,
save=False, debug=True):
"""
Aligns the projection image stack using the sequential
re-projection algorithm :cite:`Gursoy:17`.
Parameters
----------
prj : ndarray
3D stack of projection images. The first dimension
is projection axis, second and third dimensions are
the x- and y-axes of the projection image, respectively.
ang : ndarray
Projection angles in radians as an array.
iters : scalar, optional
Number of iterations of the algorithm.
pad : list-like, optional
Padding for projection images in x and y-axes.
blur : bool, optional
Blurs the edge of the image before registration.
center: array, optional
Location of rotation axis.
algorithm : {str, function}
One of the following string values.
'art'
Algebraic reconstruction technique :cite:`Kak:98`.
'gridrec'
Fourier grid reconstruction algorithm :cite:`Dowd:99`,
:cite:`Rivers:06`.
'mlem'
Maximum-likelihood expectation maximization algorithm
:cite:`Dempster:77`.
'sirt'
Simultaneous algebraic reconstruction technique.
'tv'
Total Variation reconstruction technique
:cite:`Chambolle:11`.
'grad'
Gradient descent method with a constant step size
upsample_factor : integer, optional
The upsampling factor. Registration accuracy is
inversely propotional to upsample_factor.
rin : scalar, optional
The inner radius of blur function. Pixels inside
rin is set to one.
rout : scalar, optional
The outer radius of blur function. Pixels outside
rout is set to zero.
save : bool, optional
Saves projections and corresponding reconstruction
for each algorithm iteration.
debug : book, optional
Provides debugging info such as iterations and error.
Returns
-------
ndarray
3D stack of projection images with jitter.
ndarray
Error array for each iteration.
"""
# Needs scaling for skimage float operations.
prj, scl = scale(prj)
# Shift arrays
sx = np.zeros((prj.shape[0]))
sy = np.zeros((prj.shape[0]))
conv = np.zeros((iters))
# Pad images.
npad = ((0, 0), (pad[1], pad[1]), (pad[0], pad[0]))
prj = np.pad(prj, npad, mode='constant', constant_values=0)
# Register each image frame-by-frame.
for n in range(iters):
# Reconstruct image.
rec = recon(prj, ang, center=center, algorithm=algorithm)
# Re-project data and obtain simulated data.
sim = project(rec, ang, center=center, pad=False)
# Blur edges.
if blur:
_prj = blur_edges(prj, rin, rout)
_sim = blur_edges(sim, rin, rout)
else:
_prj = prj
_sim = sim
# Initialize error matrix per iteration.
err = np.zeros((prj.shape[0]))
# For each projection
for m in range(prj.shape[0]):
# Register current projection in sub-pixel precision
shift, error, diffphase = phase_cross_correlation(
_prj[m], _sim[m], upsample_factor=upsample_factor)
err[m] = np.sqrt(shift[0]*shift[0] + shift[1]*shift[1])
sx[m] += shift[0]
sy[m] += shift[1]
# Register current image with the simulated one
tform = tf.SimilarityTransform(translation=(shift[1], shift[0]))
prj[m] = tf.warp(prj[m], tform, order=5)
if debug:
print('iter=' + str(n) + ', err=' + str(np.linalg.norm(err)))
conv[n] = np.linalg.norm(err)
if save:
write_tiff(prj, fdir + '/tmp/iters/prj', n)
write_tiff(sim, fdir + '/tmp/iters/sim', n)
write_tiff(rec, fdir + '/tmp/iters/rec', n)
# Re-normalize data
prj *= scl
return prj, sx, sy, conv
def write_center(
tomo, theta, dpath='tmp/center', cen_range=None, ind=None,
mask=False, ratio=1., sinogram_order=False, algorithm='gridrec', filter_name='parzen'):
"""
Save images reconstructed with a range of rotation centers.
Helps finding the rotation center manually by visual inspection of
images reconstructed with a set of different centers.The output
images are put into a specified folder and are named by the
center position corresponding to the image.
Parameters
----------
tomo : ndarray
3D tomographic data.
theta : array
Projection angles in radian.
dpath : str, optional
Folder name to save output images.
cen_range : list, optional
[start, end, step] Range of center values.
ind : int, optional
Index of the slice to be used for reconstruction.
mask : bool, optional
If ``True``, apply a circular mask to the reconstructed image to
limit the analysis into a circular region.
ratio : float, optional
The ratio of the radius of the circular mask to the edge of the
reconstructed image.
sinogram_order: bool, optional
Determins whether data is a stack of sinograms (True, y-axis first axis)
or a stack of radiographs (False, theta first axis).
algorithm : {str, function}
One of the following string values.
'art'
Algebraic reconstruction technique :cite:`Kak:98`.
'bart'
Block algebraic reconstruction technique.
'fbp'
Filtered back-projection algorithm.
'gridrec'
Fourier grid reconstruction algorithm :cite:`Dowd:99`,
:cite:`Rivers:06`.
'mlem'
Maximum-likelihood expectation maximization algorithm
:cite:`Dempster:77`.
'osem'
Ordered-subset expectation maximization algorithm
:cite:`Hudson:94`.
'ospml_hybrid'
Ordered-subset penalized maximum likelihood algorithm with
weighted linear and quadratic penalties.
'ospml_quad'
Ordered-subset penalized maximum likelihood algorithm with
quadratic penalties.
'pml_hybrid'
Penalized maximum likelihood algorithm with weighted linear
and quadratic penalties :cite:`Chang:04`.
'pml_quad'
Penalized maximum likelihood algorithm with quadratic penalty.
'sirt'
Simultaneous algebraic reconstruction technique.
'tv'
Total Variation reconstruction technique
:cite:`Chambolle:11`.
'grad'
Gradient descent method with a constant step size
filter_name : str, optional
Name of the filter for analytic reconstruction.
'none'
No filter.
'shepp'
Shepp-Logan filter (default).
'cosine'
Cosine filter.
'hann'
Cosine filter.
'hamming'
Hamming filter.
'ramlak'
Ram-Lak filter.
'parzen'
Parzen filter.
'butterworth'
Butterworth filter.
'custom'
A numpy array of size `next_power_of_2(num_detector_columns)/2`
specifying a custom filter in Fourier domain. The first element
of the filter should be the zero-frequency component.
'custom2d'
A numpy array of size `num_projections*next_power_of_2(num_detector_columns)/2`
specifying a custom angle-dependent filter in Fourier domain. The first element
of each filter should be the zero-frequency component.
"""
tomo = dtype.as_float32(tomo)
theta = dtype.as_float32(theta)
if sinogram_order:
dy, dt, dx = tomo.shape
else:
dt, dy, dx = tomo.shape
if ind is None:
ind = dy // 2
if cen_range is None:
center = np.arange(dx / 2 - 5, dx / 2 + 5, 0.5)
else:
center = np.arange(*cen_range)
stack = dtype.empty_shared_array((len(center), dt, dx))
for m in range(center.size):
if sinogram_order:
stack[m] = tomo[ind]
else:
stack[m] = tomo[:, ind, :]
# Reconstruct the same slice with a range of centers.
rec = recon(stack,
theta,
center=center,
sinogram_order=True,
algorithm=algorithm,
filter_name=filter_name,
nchunk=1)
# Apply circular mask.
if mask is True:
rec = circ_mask(rec, axis=0)
# Save images to a temporary folder.
dpath = os.path.abspath(dpath)
if not os.path.exists(dpath):
os.makedirs(dpath)
for m in range(len(center)):
write_tiff(data=rec[m], fname=dpath, digit='{0:.2f}'.format(center[m]))
