def test_tv(self):
geom = Geometry(2)
proj_vec = Rn(geom.proj_size).element(1)
cp = ODLChambollePock(geom, proj_vec)
cp.least_squares(3, L=131.0, non_negativiy_constraint=False,
tv_norm=1,
verbose=False)
def test_adjoint_scaling_factor(self):
"""Test if back-projector A^* is adjoint of forward projector A:
<A x, y>_D = <x,A^* y>_I .
Define scaling factor as A^* = s B where is the implemented
back-projector. Thus,
s = <A x, y>_D / <x,B y>_I ,
or using y = A x
s = <A x, A x>_D / <x,B A x>_I .
"""
geom = Geometry(2)
# x = ones() and y = A x
vol_rn = Rn(geom.vol_size)
vol_rn_ones = vol_rn.element(1)
proj_rn = Rn(geom.proj_size)
projector = ODLProjector(geom, vol_rn, proj_rn)
proj = projector.forward(vol_rn_ones)
vol = projector.backward(proj)
s0 = proj.norm() ** 2 / vol_rn._inner(vol, vol_rn_ones)
# x = ones(), y = ones()
vol_rn = Rn(geom.vol_size)
vol_rn_ones = vol_rn.element(1)
proj_rn = Rn(geom.proj_size)
proj_rn_ones = proj_rn.element(1)
projector = ODLProjector(geom, vol_rn, proj_rn)
proj = projector.forward(vol_rn_ones)
vol = projector.backward(proj_rn_ones)
s1 = proj.inner(proj_rn_ones) / vol_rn_ones.inner(vol)
# implemented function
proj_vec = Rn(geom.proj_size).element(1)
cp = ODLChambollePock(geom, proj_vec)
cp.adjoint_scaling_factor()
s2 = cp.adj_scal_fac
self.assertEqual(s1, s2)
print('Scaling factors:', s0, s1, s2)
projector.clear_astra_memory()
def test_creation_of_vector_in_rn(self):
geom = Geometry(2)
rn = Rn(geom.proj_size)
self.assertEqual(type(rn).__name__, 'Rn')
rn_vec = rn.element(np.zeros(geom.proj_size))
self.assertEqual(type(rn_vec).__name__, 'Vector')
self.assertEqual(rn.dtype, 'float')
self.assertEqual(rn.field, odl.RealNumbers())
ODLChambollePock(geom)
def test_least_squares_method(self):
geom = Geometry(2)
proj_vec = Rn(geom.proj_size).element(1)
cp = ODLChambollePock(geom, proj_vec)
num_iter = 3
cp.least_squares(num_iter, verbose=False)
def test_matrix_norm(self):
"""Compute matrix norm of forward/backward projector using power
norm. """
geom = Geometry(2)
proj_vec = Rn(geom.proj_size).element(1)
# Compute norm for simple least squares
cp = ODLChambollePock(geom, proj_vec)
self.assertEqual(cp.adj_scal_fac, 1)
mat_norm0 = cp.matrix_norm(iterations=4,
vol_init=1,
intermediate_results=True)
self.assertTrue(mat_norm0[-1] > 0)
# Resume computation
mat_norm1, vol = cp.matrix_norm(iterations=3,
vol_init=1, intermediate_results=True,
return_volume=True)
mat_norm2 = cp.matrix_norm(iterations=4, vol_init=vol,
intermediate_results=True)
self.assertNotEqual(mat_norm0[0], mat_norm2[0])
self.assertEqual(mat_norm0[3], mat_norm2[0])
# Compute norm for TV
mat_norm3 = cp.matrix_norm(iterations=4, vol_init=1, tv_norm=True,
intermediate_results=True)
self.assertFalse(np.array_equal(mat_norm2, mat_norm3))
print('LS unit init volume:', mat_norm2)
print('TV unit init volume:', mat_norm3)
# Use non-homogeneous initial volume
v0 = np.random.rand(geom.vol_size)
mat_norm4 = cp.matrix_norm(iterations=4, vol_init=v0, tv_norm=False,
intermediate_results=True)
mat_norm5 = cp.matrix_norm(iterations=4, vol_init=v0, tv_norm=True,
intermediate_results=True)
print('LS random init volume:', mat_norm4)
print('TV random init volume:', mat_norm5)
# test with adjoint scaling factor for backprojector
self.assertEqual(cp.adj_scal_fac, 1)
cp.adjoint_scaling_factor()
self.assertFalse(cp.adj_scal_fac == 1)
print('adjoint scaling factor:', cp.adj_scal_fac)
mat_norm6 = cp.matrix_norm(iterations=4, vol_init=1, tv_norm=False,
intermediate_results=True)
mat_norm7 = cp.matrix_norm(iterations=4, vol_init=1, tv_norm=True,
intermediate_results=True)
print('LS init volume, adjoint rescaled:', mat_norm6)
print('TV init volume, adjoint rescaled:', mat_norm7)