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 = register_translation(
_prj[m], _sim[m], 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:
dxchange.write_tiff(prj, fdir + '/tmp/iters/prj/prj')
dxchange.write_tiff(sim, fdir + '/tmp/iters/sim/sim')
dxchange.write_tiff(rec, fdir + '/tmp/iters/rec/rec')
# Re-normalize data
prj *= scl
return prj, sx, sy, conv
def align_seq(prj,
ang,
fdir='.',
iters=10,
pad=(0, 0),
blur=True,
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.
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)
#prj = np.pad(prj, npad, mode='edge')
# Register each image frame-by-frame.
for n in range(iters):
# Reconstruct image.
rec = recon(prj, ang, algorithm='sirt')
# Re-project data and obtain simulated data.
sim = project(rec, ang, pad=False)
# Blur edges.
if blur:
_prj = blur_edges(prj, 0.1, 0.5)
_sim = blur_edges(sim, 0.1, 0.5)
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 = register_translation(_prj[m], _sim[m], 2)
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)
##prj[m] = tf.warp(prj[m], tform, order=0, mode='edge')
if debug:
print('iter=' + str(n) + ', err=' + str(np.linalg.norm(err)))
conv[n] = np.linalg.norm(err)
if save:
dxchange.write_tiff(prj, fdir + '/tmp/iters/prj/prj')
dxchange.write_tiff(sim, fdir + '/tmp/iters/sim/sim')
dxchange.write_tiff(rec, fdir + '/tmp/iters/rec/rec')
# Re-normalize data
prj *= scl
return prj, sx, sy, conv
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 = register_translation(
_prj[m], _sim[m], 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:
dxchange.write_tiff(prj, fdir + '/tmp/iters/prj/prj')
dxchange.write_tiff(sim, fdir + '/tmp/iters/sim/sim')
dxchange.write_tiff(rec, fdir + '/tmp/iters/rec/rec')
# Re-normalize data
prj *= scl
return prj, sx, sy, conv
def align_seq(
prj, ang, fdir='.', iters=10, pad=(0, 0),
blur=True, 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.
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, algorithm='sirt')
# Re-project data and obtain simulated data.
sim = project(rec, ang, pad=False)
# Blur edges.
if blur:
_prj = blur_edges(prj, 0.1, 0.5)
_sim = blur_edges(sim, 0.1, 0.5)
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 = register_translation(_prj[m], _sim[m], 2)
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:
dxchange.write_tiff(prj, fdir + '/tmp/iters/prj/prj')
dxchange.write_tiff(sim, fdir + '/tmp/iters/sim/sim')
dxchange.write_tiff(rec, fdir + '/tmp/iters/rec/rec')
# Re-normalize data
prj *= scl
return prj, sx, sy, conv
