def setUp(self):
# Timing
self.start_time = time.time()
# DATA
self.d = ctdata.sets[14]
self.d.load()
# Parameters
det_row_count, num_proj, det_col_count = self.d.shape
num_voxel = (det_col_count, det_col_count, det_row_count)
# voxel_size = 1
voxel_size = 2 * self.d.roi_cubic_width_mm / num_voxel[0]
source_origin = self.d.distance_source_origin_mm / voxel_size
origin_detector = self.d.distance_origin_detector_mm / voxel_size
angles = self.d.angles_rad
det_col_spacing = self.d.detector_width_mm / det_col_count / voxel_size
det_row_spacing = det_col_spacing
# PROJECTOR
self.projector = Projector(
num_voxel=num_voxel,
det_row_count=det_row_count, det_col_count=det_col_count,
source_origin=source_origin, origin_detector=origin_detector,
det_row_spacing=det_row_spacing, det_col_spacing=det_col_spacing,
angles=angles)
# ALGORITHM
self.cgm = ChanGolubMullet(projections=self.d.projections,
projector=self.projector)
self.u_shape = num_voxel
def __init__(self, projections=np.array([]), projector=Projector()):
self.z = projections
self.K = projector
self.a = 1
self.u = np.zeros(projector.num_voxel)
self.w = [self.u for _ in range(self.u.ndim)]
self.b = 1
def test_adjoint_scaling(self):
vol_rn = Rn(self.geom.vol_size)
vol_rn_ones = vol_rn.element(1)
proj_rn = Rn(self.geom.proj_size)
proj_rn_ones = proj_rn.element(1)
projector = Projector(self.geom, vol_rn, proj_rn)
proj1 = projector.forward(vol_rn_ones)
vol1 = projector.backward(proj_rn_ones)
n1 = proj1.inner(proj_rn_ones)
n2 = vol_rn_ones.inner(vol1)
print('<A x, y> = <x, Ad y> : {0} = {1}'.format(n1, n2))
print('<A x, y> / <x, Ad y> - 1 = {0}'.format(n1 / n2 - 1))
proj = projector.forward(vol_rn_ones)
vol = projector.backward(proj)
alpha = proj.norm()**2 / vol_rn._inner(vol, vol_rn_ones)
print alpha
projector.clear_astra_memory()
def test_ndim(self):
vshape = (88, 77)
vsize = np.prod(vshape)
cols = 99
angles = np.linspace(0, 2 * np.pi, 111, endpoint=False)
psize = cols * np.size(angles)
geom = Geometry(geometry_type='parallel',
scale_factor=1,
volume_shape=vshape,
det_col_count=cols,
det_row_count=1,
angles=angles)
print 'Vol size: ', vsize
print 'Proj size:', psize
print 'Voxel size:', self.geom.voxel_size
vol_rn = Rn(vsize)
proj_rn = Rn(psize)
projector = Projector(geom, vol_rn, proj_rn)
proj = projector.forward(vol_rn.element(1))
p = proj.data.reshape(geom.proj_shape)
print 'Proj at 0 degree: max = ', p[0, :].max()
vol = projector.backward(proj_rn.element(1))
print vol.data.max()
projector.clear_astra_memory()
def test_gui(self):
num_iter = 8
u, p, cpd, l2_atp = ChambollePock(
projections=np.ones((100, 180, 100)),
projector=Projector()).least_squares(
num_iterations=num_iter,
L=363.569641113,
verbose=True,
non_negativiy_constraint=True)
self.assertEqual(u.__class__.__name__, 'ndarray')
self.assertEqual(cpd.size, num_iter)
self.assertEqual(l2_atp.size, num_iter)
def test_odlprojector_instance(self):
# Create cubic unit volume
vol_rn = Rn(self.geom.vol_size)
vol = np.ones(self.geom.vol_shape)
vol_rn_vec = vol_rn.element(vol.ravel())
# Create projections
proj_rn = Rn(self.geom.proj_size)
proj = np.ones(self.geom.proj_size)
proj_rn_vec = proj_rn.element(proj.ravel())
vol_norm_0 = vol_rn_vec.norm()
self.assertEqual(vol_norm_0**2, np.sqrt(self.geom.vol_size)**2)
proj_norm_0 = proj_rn_vec.norm()
self.assertEqual(proj_norm_0**2, np.sqrt(self.geom.proj_size)**2)
# ODLProjector instance
projector = Projector(self.geom, vol_rn, proj_rn)
proj_rn_vec = projector.forward(vol_rn_vec)
proj_norm_1 = proj_rn_vec.norm()
self.assertNotEqual(proj_norm_0, proj_norm_1)
vol_rn_vec = projector.backward(proj_rn_vec)
vol_norm_1 = vol_rn_vec.norm()
self.assertNotEqual(vol_norm_0, vol_norm_1)
proj_rn_vec = projector.forward(vol_rn_vec)
proj_norm_2 = proj_rn_vec.norm()
self.assertNotEqual(proj_norm_1, proj_norm_2)
vol_rn_vec = projector.backward(proj_rn_vec)
vol_norm_2 = vol_rn_vec.norm()
self.assertNotEqual(vol_norm_2, vol_norm_1)
projector.clear_astra_memory()
print 'vol norms:', vol_norm_0, vol_norm_1, vol_norm_2
print 'proj norms', proj_norm_0, proj_norm_1, proj_norm_2
def adjoint_scaling_factor(self):
"""Compute scaling factor of adjoint projector. Consider A x = y,
the adjoint A* of A is defined as:
<A x, y>_D = <x, A* y>_I
Assume A* = s B with B being the ASTRA backprojector, then:
s = <A x, A x> / <B A x, x>
Returns
-------
:rtype: float
:returns: s
"""
vol_rn = Rn(self.geom.vol_size)
proj_rn = Rn(self.geom.proj_size)
vol_rn_ones = vol_rn.element(1)
proj_rn_ones = proj_rn.element(1)
# projector = Projector(self.geom, vol_rn, proj_rn)
projector = Projector(self.geom)
proj = projector.forward(vol_rn_ones)
vol = projector.backward(proj_rn_ones)
# print vol.data.min(), vol.data.max()
# print proj.data.min(), proj.data.max()
self.adj_scal_fac = proj.inner(proj_rn_ones) / vol_rn_ones.inner(vol)
# self.adj_scal_fac = proj.norm()**2 / vol_rn.inner(vol, vol_rn_ones)
# return proj.norm()**2 / vol_rn._inner(vol, vol_rn_ones)
projector.clear_astra_memory()
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 least_squares(self,
iterations=1,
L=None,
tau=None,
sigma=None,
theta=None,
non_negativiy_constraint=False,
tv_norm=False,
verbose=True):
"""Least-squares problem with optional TV-regularisation and/or
non-negativity constraint.
Parameters
----------
:type iterations: int (default 1)
:param iterations: Number of iterations the optimization should
run for.
:type L: float (defaul: None)
:param L: Matrix norm of forward projector. If 'None' matrix_norm is
called with 20 iterations.
:type tau: float (default 1/L)
:param tau:
:type sigma: float (default 1/L)
:param sigma:
:type theta: float (default 1)
:param theta:
:type non_negativiy_constraint: bool (default False)
:param non_negativiy_constraint: Add non-negativity constraint to
optimization problem (via indicator function).
:type tv_norm: bool | float (default False)
:param tv_norm: Unless False, coincides with the numerical value of
the parameter lambda for TV-Regularisation.
:type verbose: bool (default False)
:param verbose: Show intermediate reconstructions and
convergence measures during iteration.
Returns
-------
:rtype: odl.Vector, odl.Vector, numpy.ndarray, numpy.ndarray
:returns: u, p, cpd, l2_du
u: vector of reconstructed volume
p: vector of dual projection variable
cpd: condition primal-dual gap (convergence measure)
l2_du: l2-norm of constraint-induced convergence measure
"""
# step 1:
if L is None:
L = self.matrix_norm(20)
if tau is None:
tau = 1 / L
if sigma is None:
sigma = 1 / L
if theta is None:
theta = 1
# print 'tau:', tau
# print 'sigma:', sigma
# print 'theta:', theta
geom = self.geom
g = self.proj # domain: D
# l2-norm of (volume update / tau)
l2_du = np.zeros(iterations)
# conditional primal-dual gap
cpd = np.zeros(iterations)
# step 2: initialize u and p with zeros
u = self.recon_space.zero() # domain: I
p = g.space.zero() # domain: D
# q: spatial vector = list of ndarrays in I (not Rn vectors)
if tv_norm:
ndim = geom.vol_ndim
# domain of q: V = [I, I, ...]
q = [
np.zeros(geom.vol_shape, dtype=u.data.dtype)
for _ in range(ndim)
]
# step 3: ub <- u
ub = u.copy() # domain: I
# initialize projector
# A = Projector(geom, u.space, p.space)
A = Projector(geom)
# visual output instance
disp = DisplayIntermediates(verbose=verbose,
vol=u.data.reshape(geom.vol_shape),
cpd=cpd,
l2_du=l2_du)
# step 4: repeat
for n in range(iterations):
# step 5: p_{n+1} <- (p_n + sigma(A^T ub_n - g)) / (1 + sigma)
if n >= 0:
# with(Timer('proj:')):
# # p_tmp <- A ub
# p_tmp = A.forward(ub)
# # p_tmp <- p_tmp - g
# p_tmp -= g
# # p <- p + sigma * p_tmp
# p += sigma * p_tmp
# p_n <- p_n + sigma(A ub -g )
tmp = A.forward(ub)
# print 'p:', p.data.shape, 'Au:', tmp.data.shape, 'g:', \
# g.data.shape
p += sigma * (A.forward(ub) - g)
else:
p -= sigma * g
# p <- p / (1 + sigma)
p /= 1 + sigma
# TV step 6: q_{n+1} <- lambda(q_n + sigma grad ub_n) /
# max(lambda 1_I, |q_n + sigma grad ub_n|)
if tv_norm:
for dim in range(ndim):
# q_n <- q_n + sigma * grad ub_n
q[dim] += sigma * partial(
ub.data.reshape(self.geom.vol_shape), dim,
geom.voxel_width[dim])
# |q_n|: isotropic TV
# use div_q to save memory, q = [qi] where qi are ndarrays
div_q = np.sqrt(reduce(add, (qi**2 for qi in q)))
# max(lambda 1_I, |q_n + sigma diff ub_n|)
# print 'q_mag:', div_q.min(), div_q.max()
div_q[div_q < tv_norm] = tv_norm
# q_n <- lambda * q_n / |q_n|
for dim in range(ndim):
q[dim] /= div_q
q[dim] *= tv_norm
# div q_{n+1}
div_q = reduce(add, (partial(qi, dim, geom.voxel_width[dim])
for (dim, qi) in enumerate(q)))
div_q *= tau
# step 6: u_{n+1} <- u_{n} - tau * A^T p_{n+1}
# TV step 7: u_{n+1} <- u_{n} - tau * A^T p_{n+1} + div q_{n+1}
# ub_tmp <- A^T p
ub_tmp = A.backward(p)
ub_tmp *= tau
ub_tmp *= self.adj_scal_fac
# l2-norm per voxel of ub_tmp = A^T p
l2_du[n:] = ub_tmp.norm() # / u.data.size
if tv_norm:
l2_du[n:] += np.linalg.norm(div_q.ravel()) # / u.data.size
# store current u_n temporarily in ub_n
ub = -u.copy()
# u <- u - tau ub_tmp
u -= ub_tmp
# TV: u <- u + tau div q
if tv_norm:
print('{0}: u - A^T p: min = {1}, max = {2}'.format(
n, u.data.min(), u.data.max()))
print('{0}: div q: min = {1}, max = {2}'.format(
n, div_q.min(), div_q.max()))
u.data[:] += div_q.ravel()
# Positivity constraint
if non_negativiy_constraint:
u.data[u.data < 0] = 0
# print '\nu:', u.data.min(), u.data.max()
# conditional primal-dual gap for current u and p
# 1/2||A u - g||_2^2 + 1/2||p||_2^2 + <p,g>_D
# p_tmp <- A u
# p_tmp = A.forward(u)
# p_tmp -= g
# cpd[n:] = (0.5 * p_tmp.norm() ** 2 +
cpd[n:] = (0.5 * p.space.norm(A.forward(u) - g)**2 +
0.5 * p.norm()**2 + p.inner(g)) # / p.data.size
if tv_norm:
cpd[n:] += tv_norm * np.linalg.norm(reduce(
add, (partial(u.data.reshape(geom.vol_shape), dim,
geom.voxel_width[dim])
for dim in range(geom.vol_ndim))).ravel(),
ord=1) # / u.data.size
# step 7 / TV step 8: ub_{n+1} <- u_{n+1} + theta(u_{n+1} - u_n)
# ub <- ub + u_{n+1}, remember ub = -u_n
ub += u
# ub <- theta * ub
ub *= theta
# ub <- ub + u_{n+1}
ub += u
# visual output
disp.update()
A.clear_astra_memory()
# Should avoid window freezing
disp.show()
return u, p, cpd, l2_du
class ChanGolubMulletTestCase(unittest.TestCase):
def setUp(self):
# Timing
self.start_time = time.time()
# DATA
self.d = ctdata.sets[14]
self.d.load()
# Parameters
det_row_count, num_proj, det_col_count = self.d.shape
num_voxel = (det_col_count, det_col_count, det_row_count)
# voxel_size = 1
voxel_size = 2 * self.d.roi_cubic_width_mm / num_voxel[0]
source_origin = self.d.distance_source_origin_mm / voxel_size
origin_detector = self.d.distance_origin_detector_mm / voxel_size
angles = self.d.angles_rad
det_col_spacing = self.d.detector_width_mm / det_col_count / voxel_size
det_row_spacing = det_col_spacing
# PROJECTOR
self.projector = Projector(
num_voxel=num_voxel,
det_row_count=det_row_count, det_col_count=det_col_count,
source_origin=source_origin, origin_detector=origin_detector,
det_row_spacing=det_row_spacing, det_col_spacing=det_col_spacing,
angles=angles)
# ALGORITHM
self.cgm = ChanGolubMullet(projections=self.d.projections,
projector=self.projector)
self.u_shape = num_voxel
def tearDown(self):
# Timing
t = time.time() - self.start_time
print "%s: %.3f" % (self.id(), t)
# Clear ASTRA memory
self.projector.clear()
def test_initialization(self):
self.assertTrue(issubclass(type(self.cgm), object))
def test_g(self):
g = self.cgm.g
u_shape = self.cgm.K.volume_shape
self.assertEqual(g.__class__.__name__, 'ndarray')
self.assertEqual(np.shape(g), tuple((x - 0 for x in u_shape)))
def test_f(self):
f = self.cgm.f
fl = list(f)
# ft = tuple(f)
self.assertEqual(len(fl), len(self.d.shape))
# self.assertEqual(type(f), list)
def test_func_du(self):
func_du = self.cgm.func_du(np.zeros(self.u_shape))
self.assertEqual(func_du.shape, self.u_shape)
self.assertTrue(func_du.any() == 0)
class ChambollePockTestCase(unittest.TestCase):
"""Test case for primal-dual method Chambolle-Pock algorithm."""
def setUp(self):
# Timing
self.start_time = time.time()
# DATA
self.d = ctdata.sets[14]
self.d.load()
# Parameters
det_row_count, num_proj, det_col_count = self.d.shape
num_voxel = (det_col_count, det_col_count, det_row_count)
voxel_size = 2 * self.d.roi_cubic_width_mm / num_voxel[0]
source_origin = self.d.distance_source_origin_mm / voxel_size
origin_detector = self.d.distance_origin_detector_mm / voxel_size
angles = self.d.angles_rad
det_col_spacing = self.d.detector_width_mm / det_col_count / voxel_size
det_row_spacing = det_col_spacing
# PROJECTOR
self.projector = Projector(
num_voxel=num_voxel,
det_row_count=det_row_count, det_col_count=det_col_count,
source_origin=source_origin, origin_detector=origin_detector,
det_row_spacing=det_row_spacing, det_col_spacing=det_col_spacing,
angles=angles)
# ALGORITHM
self.pc = ChambollePock(projections=self.d.projections,
projector=self.projector)
self.u_shape = num_voxel
def tearDown(self):
# Timing
t = time.time() - self.start_time
print "%s: %.3f" % (self.id(), t)
# Clean ASTRA memory
self.projector.clear()
def test_projection_data(self):
d = self.d.projections
print 'min:', d.min(), 'max:', d.max(), 'mean:', np.mean(d)
self.assertTrue(self.d.projections.min() > 0)
self.assertTrue(self.d.projections.max() < np.inf)
def test_initialization(self):
self.assertTrue(self.d.projections.shape > 0)
self.assertTrue(self.pc.K.volume_data)
self.pc.K.backward()
# self.assertEqual(str(self.d.dtype), 'uint16')
self.assertEqual(str(self.d.dtype), 'float32')
self.assertEqual(self.pc.K.volume_data.dtype.__str__(), 'float32')
self.assertTrue(self.pc.K.volume_shape > 0)
self.assertTrue(issubclass(type(self.pc), object))
self.assertEqual(self.pc.K, self.projector)
def test_matrix_norm(self):
# Start computation of matrix
num_iter = 2
mat_norm_list = self.pc.matrix_norm(
num_iter, vol_init=1, intermediate_results=True)
self.assertEqual(np.size(mat_norm_list), num_iter)
# Continue iteration of matrix, starting from the above results
mat_norm = self.pc.matrix_norm(3, continue_iteration=True)
self.assertEqual(np.size(mat_norm), 1)
self.assertTrue(mat_norm > 0)
self.assertNotEqual(mat_norm_list[-1], mat_norm)
mat_norm = self.pc.matrix_norm(20, vol_init=1,
intermediate_results=True)
self.pc.K.clear()
print mat_norm
def test_least_squares(self):
num_iter = 10
u, p, cpd, l2_atp = self.pc.least_squares(
num_iterations=num_iter,
L=363.569641113,
verbose=True,
non_negativiy_constraint=False)
self.assertEqual(u.__class__.__name__, 'ndarray')
self.assertEqual(cpd.size, num_iter)
self.assertEqual(l2_atp.size, num_iter)
self.pc.K.clear()
def test_least_squares_with_non_negativity_constraint(self):
num_iter = 4
u, p, cpd, l2_atp = self.pc.least_squares(
num_iterations=num_iter,
L=363.569641113,
verbose=True,
non_negativiy_constraint=True)
self.assertEqual(u.__class__.__name__, 'ndarray')
self.assertEqual(cpd.size, num_iter)
self.assertEqual(l2_atp.size, num_iter)
self.pc.K.clear()
def __init__(self, projections=np.array([]), projector=Projector()):
self.y = projections.astype('float32', copy=False)
self.K = projector
# Parameters
num_iter = 50
det_row_count, num_proj, det_col_count = d.shape
num_voxel = (det_col_count, det_col_count, det_row_count)
# voxel_size = 1
voxel_size = 2 * d.roi_cubic_width_mm / num_voxel[0]
source_origin = d.distance_source_origin_mm / voxel_size
origin_detector = d.distance_origin_detector_mm / voxel_size
angles = d.angles_rad
det_col_spacing = d.detector_width_mm / det_col_count / voxel_size
det_row_spacing = det_col_spacing
# Projector instance
p = Projector(num_voxel=num_voxel,
det_row_count=det_row_count, det_col_count=det_col_count,
source_origin=source_origin, origin_detector=origin_detector,
det_row_spacing=det_row_spacing, det_col_spacing=det_col_spacing,
angles=angles)
# Create row sums of system matrix
p.set_volume_data(1)
p.forward()
# rs = p.projection_data.copy()
row_sum = p.projection_data
row_sum[row_sum > 0] = 1.0 / row_sum[row_sum > 0]
# Create colum sums of system matrix
p.set_projection_data(1)
p.backward()
# cs = p.volume_data.copy()
col_sum = p.volume_data
