def test_comp_proj():
r3 = odl.rn(3)
r3xr3 = odl.ProductSpace(r3, 2)
x = r3xr3.element([[1, 2, 3], [4, 5, 6]])
proj_0 = odl.ComponentProjection(r3xr3, 0)
assert x[0] == proj_0(x)
assert x[0] == proj_0(x, out=proj_0.range.element())
proj_1 = odl.ComponentProjection(r3xr3, 1)
assert x[1] == proj_1(x)
assert x[1] == proj_1(x, out=proj_1.range.element())
def test_comp_proj_adjoint():
r3 = odl.rn(3)
r3xr3 = odl.ProductSpace(r3, 2)
x = r3.element([1, 2, 3])
result_0 = r3xr3.element([[1, 2, 3], [0, 0, 0]])
proj_0 = odl.ComponentProjection(r3xr3, 0)
assert result_0 == proj_0.adjoint(x)
assert result_0 == proj_0.adjoint(x, out=proj_0.domain.element())
result_1 = r3xr3.element([[0, 0, 0], [1, 2, 3]])
proj_1 = odl.ComponentProjection(r3xr3, 1)
assert result_1 == proj_1.adjoint(x)
assert result_1 == proj_1.adjoint(x, out=proj_1.domain.element())
def test_comp_proj_indices():
r3 = odl.rn(3)
r33 = odl.ProductSpace(r3, 3)
x = r33.element([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
proj = odl.ComponentProjection(r33, [0, 2])
assert x[[0, 2]] == proj(x)
assert x[[0, 2]] == proj(x, out=proj.range.element())
def test_comp_proj_slice():
r3 = odl.Rn(3)
r33 = odl.ProductSpace(r3, 3)
x = r33.element([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
proj = odl.ComponentProjection(r33, slice(0, 2))
assert x[0:2] == proj(x)
assert x[0:2] == proj(x, out=proj.range.element())
def test_comp_proj_adjoint_slice():
r3 = odl.rn(3)
r33 = odl.ProductSpace(r3, 3)
x = r33[0:2].element([[1, 2, 3], [4, 5, 6]])
result = r33.element([[1, 2, 3], [4, 5, 6], [0, 0, 0]])
proj = odl.ComponentProjection(r33, slice(0, 2))
assert result == proj.adjoint(x)
assert result == proj.adjoint(x, out=proj.domain.element())
def tnv(operator, data, alpha, sinfo, eta, nonneg=True, datafit=None):
space = operator.domain
grad = odl.Gradient(space)
P = odl.ComponentProjection(grad.range**2, 0)
D = P.adjoint * grad
Q = odl.ComponentProjection(grad.range**2, 1)
A = odl.BroadcastOperator(operator, D)
F1 = get_data_fit(datafit, data)
N = odl.solvers.NuclearNorm(D.range, outer_exp=1, singular_vector_exp=1)
F2 = alpha * N.translated(-Q.adjoint(eta * grad(sinfo)))
F = odl.solvers.SeparableSum(F1, F2)
if nonneg:
G = odl.solvers.IndicatorNonnegativity(space)
else:
G = odl.solvers.ZeroFunctional(space)
return G, F, A
# Initialize gradient operator
gradient = odl.Gradient(reco_space, method='forward')
gradient_back = odl.Gradient(reco_space, method='backward')
eps = odl.DiagonalOperator(gradient_back, reco_space.ndim)
# Create the domain of the problem, given by the reconstruction space and the
# range of the gradient on the reconstruction space.
domain = odl.ProductSpace(reco_space, gradient.range)
# Column vector of three operators defined as:
# 1. Computes ``A(x)``
# 2. Computes ``grad(x) - y``
# 3. Computes ``eps(y)``
op = odl.BroadcastOperator(
ray_trafo * odl.ComponentProjection(domain, 0),
odl.ReductionOperator(gradient, odl.ScalingOperator(gradient.range, -1)),
eps * odl.ComponentProjection(domain, 1))
# Do not use the g functional, set it to zero.
g = odl.solvers.ZeroFunctional(op.domain)
# Create functionals for the dual variable
# l2-squared data matching
l2_norm = odl.solvers.L2NormSquared(ray_trafo.range).translated(data)
# The l1-norms scaled by regularization paramters
l1_norm_1 = 0.001 * odl.solvers.L1Norm(gradient.range)
l1_norm_2 = 1e-4 * odl.solvers.L1Norm(eps.range)
noisy_data,
niter=10,
callback=callback)
multigrid.graphics.show_both(*reco)
elif reco_method == 'TV':
insert_grad = odl.Gradient(insert_discr, pad_mode='order1')
coarse_grad = odl.Gradient(coarse_discr, pad_mode='order1')
# Differentiable part, build as ||. - g||^2 o P
data_func = odl.solvers.L2NormSquared(
sum_ray_trafo.range).translated(noisy_data) * sum_ray_trafo
reg_param_1 = 8e-3
reg_func_1 = reg_param_1 * (odl.solvers.L2NormSquared(coarse_discr) *
odl.ComponentProjection(pspace, 0))
smooth_func = data_func + reg_func_1
# Non-differentiable part composed with linear operators
reg_param = 8e-3
nonsmooth_func = reg_param * odl.solvers.L1Norm(insert_grad.range)
if iter == 0:
reg_param_2 = 8e-2
elif iter == 1:
reg_param_2 = 8e-3
elif iter == 2:
reg_param_2 = 8e-4
elif iter == 3:
reg_param_2 = 8e-5
elif iter == 4:
# D = data matching functional: Y1 x Y2 -> R, ||. - g1||_Y1^2 + ||. - g2||_Y2^2 # S1 = squared L2-norm: X1^2 -> R, for Tikhonov functional # S2 = (alpha * L12-Norm): X2^2 -> R, for isotropic TV # Operators # A = forward operator "matrix": X1 x X2 -> Y1 x Y2 # G1 = spatial gradient: X1 -> X1^2 # G2 = spatial gradient: X2 -> X2^2 # B1 = G1 extended to X1 x X2, B1(f1, f2) = G1(f1) # B2 = G2 extended to X1 x X2, B2(f1, f2) = G2(f2) A = odl.ProductSpaceOperator([[R11, 0], [A21, R22]]) G1 = odl.Gradient(X1, pad_mode='symmetric') G2 = odl.Gradient(X2, pad_mode='order1') # Extend gradients to product space B1 = G1 * odl.ComponentProjection(A.domain, 0) B2 = G2 * odl.ComponentProjection(A.domain, 1) # TODO: weighting for differences in sizes (avoid large region domination) D = odl.solvers.L2NormSquared(A.range).translated([g1, g2]) # For isotropic TV # alpha1 = 1e-2 # S1 = alpha1 * odl.solvers.GroupL1Norm(G1.range) # For Tikhonov alpha1 = 1e-2 S1 = alpha1 * odl.solvers.L2NormSquared(G1.range) # TV on second component alpha2 = 1e-4 S2 = alpha2 * odl.solvers.GroupL1Norm(G2.range)
#sym_gradient = odl.operator.ProductSpaceOperator(
# [[Dx, 0], [0, Dy], [0.5*Dy, 0.5*Dx]], range=W)
E = odl.operator.ProductSpaceOperator(
[[Dx, 0], [0, Dy], [0.5*Dy, 0.5*Dx], [0.5*Dy, 0.5*Dx]])
W = E.range
# Create the domain of the problem, given by the reconstruction space and the
# range of the gradient on the reconstruction space.
domain = odl.ProductSpace(U, V)
# Column vector of three operators defined as:
# 1. Computes ``Ax``
# 2. Computes ``Gx - y``
# 3. Computes ``Ey``
op = odl.BroadcastOperator(
A * odl.ComponentProjection(domain, 0),
odl.ReductionOperator(G, odl.ScalingOperator(V, -1)),
E * odl.ComponentProjection(domain, 1))
# Do not use the g functional, set it to zero.
g = odl.solvers.ZeroFunctional(domain)
# l2-squared data matching
l2_norm = odl.solvers.L2NormSquared(A.range).translated(data)
# parameters
alpha = 1e-1
beta = 1
# The l1-norms scaled by regularization paramters
l1_norm_1 = alpha * odl.solvers.L1Norm(V)
# Initialize gradient and 2nd order derivative operator
gradient = odl.Gradient(reco_space)
eps = odl.DiagonalOperator(gradient, reco_space.ndim)
domain = odl.ProductSpace(gradient.domain, eps.domain)
# Assemble operators and functionals for the solver
# The linear operators are
# 1. identity on the first component for the data matching
# 2. gradient of component 1 - component 2 for the auxiliary functional
# 3. eps on the second component
# 4. projection onto the first component
lin_ops = [
odl.ComponentProjection(domain, 0),
odl.ReductionOperator(gradient, odl.ScalingOperator(gradient.range, -1)),
eps * odl.ComponentProjection(domain, 1),
odl.ComponentProjection(domain, 0)
]
# The functionals are
# 1. L2 data matching
# 2. regularization parameter 1 times L1 norm on the range of the gradient
# 3. regularization parameter 2 times L1 norm on the range of eps
# 4. box indicator on the reconstruction space
data_matching = odl.solvers.L2NormSquared(reco_space).translated(data)
reg_param1 = 4e0
regularizer1 = reg_param1 * odl.solvers.L1Norm(gradient.range)
reg_param2 = 1e0
R2 = odl.tomo.RayTransform(X2, geometry)
M = odl_multigrid.MaskingOperator(X1, roi_min_pt, roi_max_pt)
A1 = R1 * M
A2 = R2
A = odl.ReductionOperator(A1, A2)
G1 = odl.Gradient(X1, pad_mode='symmetric')
G2 = odl.Gradient(X2, pad_mode='order1')
alpha1 = 1e0
alpha2 = 5e-2
S1 = alpha1 * odl.solvers.L2NormSquared(G1.range)
S2 = alpha2 * odl.solvers.GroupL1Norm(G2.range)
B1 = G1 * odl.ComponentProjection(X1 * X2, 0)
B2 = G2 * odl.ComponentProjection(X1 * X2, 1)
D = odl.solvers.L2NormSquared(A.range).translated(y)
# We check how much we gained regarding runtimes:
get_ipython().run_line_magic('timeit', 'A(A.domain.zero())')
get_ipython().run_line_magic('timeit', 'A.adjoint(A.range.zero())')
# The forward operator is not so much faster, since we still have the same
# number of rays to compute, i.e., forward projection scales with the number
# of angles and detector pixels. That is something to improve later.
# However, the adjoint is much faster since it scales with the number voxels.
# Now we do the usual steps and reconstruct:
else:
odl.solvers.conjugate_gradient_normal(ray_trafo_combined,
reco,
data,
niter=niter_cg,
callback=callback)
multigrid.graphics.show_both(*reco)
elif reco_method == 'TV':
grad_detail = odl.Gradient(space_detail, pad_mode='order1')
l2_norm_sq = odl.solvers.L2NormSquared(ray_trafo_combined.range)
data_func = l2_norm_sq.translated(data)
reg_func_lowres = odl.solvers.ZeroFunctional(space_lowres)
comp_proj_lowres = odl.ComponentProjection(pspace, 0)
reg_param_detail = 3e-3
reg_func_detail = (reg_param_detail *
odl.solvers.L1Norm(grad_detail.range))
comp_proj_detail = odl.ComponentProjection(pspace, 1)
min_val, max_val = np.min(reco_fbp), np.max(reco_fbp)
box_constr = odl.solvers.IndicatorBox(pspace, min_val, max_val)
f = odl.solvers.ZeroFunctional(pspace)
L = [ray_trafo_combined, comp_proj_lowres, grad_detail * comp_proj_detail]
g = [data_func, reg_func_lowres, reg_func_detail]
ray_trafo_norm = 1.2 * odl.power_method_opnorm(ray_trafo_combined,
maxiter=4)
planes=planes)
c = float(norm_K) / float(norm_D)
D *= c
norm_D *= c
L1 = odl.solvers.SeparableSum(
*[(alpha / c) *
odl.solvers.GroupL1Norm(gradient.range), (alpha * beta / c) *
odl.solvers.GroupL1Norm(E.range)])
g = odl.solvers.SeparableSum(
odl.solvers.IndicatorBox(U, lower=0),
odl.solvers.ZeroFunctional(gradient.range))
X = D.domain
P = [odl.ComponentProjection(X, i) for i in range(2)]
A_ = odl.BroadcastOperator(K * P[0], D)
f_ = odl.solvers.SeparableSum(KL, L1)
obj_fun = f_ * A_ + g # objective functional
fldr = '{}/pics'.format(folder_param)
if not os.path.exists('{}/gray_image_pet.png'.format(fldr)):
tmp = U.element()
tmp_op = mMR.operator_mmr()
tmp_op.toodl(image, tmp)
misc.save_image(tmp.asarray(), 'image_pet', fldr, planes=planes)
tmp_op.toodl(image_mr, tmp)
misc.save_image(tmp.asarray(), 'image_mr', fldr, planes=planes)
tmp_op.toodl(image_ct, tmp)
misc.save_image(tmp.asarray(), 'image_ct', fldr, planes=planes)