def matrix_norm(self,
iterations,
vol_init=1.0,
tv_norm=False,
return_volume=False,
intermediate_results=False):
"""The matrix norm || K ||_2 of 'K' defined here as largest
singular value of 'K'. Employs the generic power method to obtain a
scalar 's' which tends to || K ||_2 as the iterations N increase.
To be implemented: optionally return volume 'x', such that it can be
re-used as initializer to continue the iteration.
Parameters
----------
:type iterations: int
:param iterations: Number of iterations of the generic power method.
:type vol_init: float | ndarray (default 1.0)
:param vol_init: in I, initial image to start with.
:type intermediate_results: bool
:param intermediate_results: Returns list of intermediate results
instead of scalar.
:type return_volume: bool
:param return_volume: Return volume in order to resume iteration via
passing it over as initial volume.
Returns
-------
:rtype: float | numpy.ndarray, numpay.array (optional)
:returns: s, vol
s: Scalar of final iteration or numpy.ndarray containing all
results during iteration.
vol: Volume vector
"""
geom = self.geom
vol = self.recon_space.element(vol_init)
proj = Rn(geom.proj_size).zero()
# projector = Projector(geom, vol.space, proj.space)
projector = Projector(geom)
# print 'projector scaling factor', projector.scal_fac
tmp = None
if intermediate_results:
s = np.zeros(iterations)
else:
s = 0
# Power method loop
for n in range(iterations):
# step 4: x_{n+1} <- K^T K x_n
if tv_norm:
# K = (A, grad) instead of K = A
# Compute: - div grad x_n
# use sum over generator expression
tmp = -reduce(add, (partial(
partial(vol.data.reshape(geom.vol_shape), dim,
geom.voxel_width[dim]), dim, geom.voxel_width[dim])
for dim in range(geom.vol_ndim)))
# x_n <- A^T (A x_n)
vol = projector.backward(projector.forward(vol))
vol *= self.adj_scal_fac
if tv_norm:
# x_n <- x_n - div grad x_n
# print 'n: {2}. vol: min = {0}, max = {1}'.format(
# vol.data.min(), vol.data.max(), n)
# print 'n: {2}. tv: min = {0}, max = {1}'.format(tmp.min(),
# tmp.max(), n)
vol.data[:] += tmp.ravel()
# step 5:
# x_n <- x_n/||x_n||_2
vol /= vol.norm()
# step 6:
# s_n <-|| K x ||_2
if intermediate_results:
# proj <- A^T x_n
proj = projector.forward(vol)
s[n] = proj.norm()
if tv_norm:
s[n] = np.sqrt(
s[n]**2 +
reduce(add, (np.linalg.norm(
partial(vol.data.reshape(geom.vol_shape), dim,
geom.voxel_width[dim]))**2
for dim in range(geom.vol_ndim))))
# step 6: || K x ||_2
if not intermediate_results:
proj = projector.forward(vol)
s = proj.norm()
if tv_norm:
s = np.sqrt(s**2 +
reduce(add, (np.linalg.norm(
partial(vol.data.reshape(geom.vol_shape), dim,
geom.voxel_width[dim]))**2
for dim in range(geom.vol_ndim))))
# Clear ASTRA memory
projector.clear_astra_memory()
# Returns
if not return_volume:
return s
else:
return s, vol.data
def matrix_norm(self, iterations, vol_init=1.0,
tv_norm=False, return_volume=False,
intermediate_results=False):
"""The matrix norm || K ||_2 of 'K' defined here as largest
singular value of 'K'. Employs the generic power method to obtain a
scalar 's' which tends to || K ||_2 as the iterations N increase.
To be implemented: optionally return volume 'x', such that it can be
re-used as initializer to continue the iteration.
Parameters
----------
:type iterations: int
:param iterations: Number of iterations of the generic power method.
:type vol_init: float | ndarray (default 1.0)
:param vol_init: in I, initial image to start with.
:type intermediate_results: bool
:param intermediate_results: Returns list of intermediate results
instead of scalar.
:type return_volume: bool
:param return_volume: Return volume in order to resume iteration via
passing it over as initial volume.
Returns
-------
:rtype: float | numpy.ndarray, numpay.array (optional)
:returns: s, vol
s: Scalar of final iteration or numpy.ndarray containing all
results during iteration.
vol: Volume vector
"""
geom = self.geom
vol = self.recon_space.element(vol_init)
proj = Rn(geom.proj_size).zero()
# projector = Projector(geom, vol.space, proj.space)
projector = Projector(geom)
# print 'projector scaling factor', projector.scal_fac
tmp = None
if intermediate_results:
s = np.zeros(iterations)
else:
s = 0
# Power method loop
for n in range(iterations):
# step 4: x_{n+1} <- K^T K x_n
if tv_norm:
# K = (A, grad) instead of K = A
# Compute: - div grad x_n
# use sum over generator expression
tmp = -reduce(add,
(partial(
partial(vol.data.reshape(geom.vol_shape),
dim, geom.voxel_width[dim]),
dim, geom.voxel_width[dim]) for dim in
range(geom.vol_ndim)))
# x_n <- A^T (A x_n)
vol = projector.backward(projector.forward(vol))
vol *= self.adj_scal_fac
if tv_norm:
# x_n <- x_n - div grad x_n
# print 'n: {2}. vol: min = {0}, max = {1}'.format(
# vol.data.min(), vol.data.max(), n)
# print 'n: {2}. tv: min = {0}, max = {1}'.format(tmp.min(),
# tmp.max(), n)
vol.data[:] += tmp.ravel()
# step 5:
# x_n <- x_n/||x_n||_2
vol /= vol.norm()
# step 6:
# s_n <-|| K x ||_2
if intermediate_results:
# proj <- A^T x_n
proj = projector.forward(vol)
s[n] = proj.norm()
if tv_norm:
s[n] = np.sqrt(s[n] ** 2 +
reduce(add,
(np.linalg.norm(
partial(vol.data.reshape(
geom.vol_shape), dim,
geom.voxel_width[dim])) ** 2
for dim in range(geom.vol_ndim))))
# step 6: || K x ||_2
if not intermediate_results:
proj = projector.forward(vol)
s = proj.norm()
if tv_norm:
s = np.sqrt(s ** 2 + reduce(add,
(np.linalg.norm(partial(
vol.data.reshape(
geom.vol_shape), dim,
geom.voxel_width[dim])) ** 2
for dim in range(geom.vol_ndim))))
# Clear ASTRA memory
projector.clear_astra_memory()
# Returns
if not return_volume:
return s
else:
return s, vol.data
