# Create space defined on a square from [0, 0] to [100, 100] with (100 x 100)
# points
space = odl.uniform_discr([0, 0], [100, 100], [100, 100])
# Create ODL operator for the Laplacian
laplacian = odl.Laplacian(space)
# Create right hand side
phantom = odl.phantom.shepp_logan(space, modified=True)
phantom.show('original image')
rhs = laplacian(phantom)
rhs += odl.phantom.white_noise(space) * np.std(rhs) * 0.1
rhs.show('rhs')
# Convert laplacian to ProxImaL operator
proximal_lang_laplacian = odl.as_proximal_lang_operator(laplacian)
# Convert to array
rhs_arr = rhs.asarray()
# Set up optimization problem
x = proximal.Variable(space.shape)
funcs = [10 * proximal.sum_squares(proximal_lang_laplacian(x) - rhs_arr),
proximal.norm1(proximal.grad(x))]
# Solve the problem using ProxImaL
prob = proximal.Problem(funcs)
prob.solve(verbose=True)
# Convert back to odl and display result
result_odl = space.element(x.value)
max_pt=[20, 20],
shape=[300, 300],
dtype='float32')
# Make a parallel beam geometry with flat detector
# Angles: uniformly spaced, n = 360, min = 0, max = pi
angle_partition = odl.uniform_partition(0, np.pi, 360)
# Detector: uniformly sampled, n = 512, min = -30, max = 30
detector_partition = odl.uniform_partition(-30, 30, 512)
geometry = odl.tomo.Parallel2dGeometry(angle_partition, detector_partition)
# Initialize the ray transform (forward projection).
ray_trafo = odl.tomo.RayTransform(reco_space, geometry)
# Convert ray transform to proximal language operator
proximal_lang_ray_trafo = odl.as_proximal_lang_operator(ray_trafo)
# Create sinogram of forward projected phantom with noise
phantom = odl.phantom.shepp_logan(reco_space, modified=True)
phantom.show('phantom')
data = ray_trafo(phantom)
data += odl.phantom.white_noise(ray_trafo.range) * np.mean(data) * 0.1
data.show('noisy data')
# Convert to array for ProxImaL
rhs_arr = data.asarray()
# Set up optimization problem
# Note that proximal is not aware of the underlying space and only works with
# matrices. Hence the norm in proximal does not match the norm in the ODL space
# exactly.
# Create space defined on a square from [0, 0] to [100, 100] with (100 x 100)
# points
space = odl.uniform_discr([0, 0], [100, 100], [100, 100])
# Create ODL operator for the Laplacian
laplacian = odl.Laplacian(space)
# Create right hand side
phantom = odl.phantom.shepp_logan(space, modified=True)
phantom.show('original image')
rhs = laplacian(phantom)
rhs += odl.phantom.white_noise(space) * np.std(rhs) * 0.1
rhs.show('rhs')
# Convert laplacian to ProxImaL operator
proximal_lang_laplacian = odl.as_proximal_lang_operator(laplacian)
# Convert to array
rhs_arr = rhs.asarray()
# Set up optimization problem
x = proximal.Variable(space.shape)
funcs = [
10 * proximal.sum_squares(proximal_lang_laplacian(x) - rhs_arr),
proximal.norm1(proximal.grad(x))
]
# Solve the problem using ProxImaL
prob = proximal.Problem(funcs)
prob.solve(verbose=True)
detector_partition = odl.uniform_partition(-30, 30, 558)
geometry = odl.tomo.Parallel2dGeometry(angle_partition, detector_partition)
# The implementation of the ray transform to use, options:
# 'scikit' Requires scikit-image (can be installed by
# running ``pip install scikit-image``).
# 'astra_cpu', 'astra_cuda' Requires astra tomography to be installed.
# Astra is much faster than scikit. Webpage:
# https://github.com/astra-toolbox/astra-toolbox
impl = 'astra_cuda'
# Initialize the ray transform (forward projection).
ray_trafo = odl.tomo.RayTransform(reco_space, geometry, impl=impl)
# Convert ray transform to proximal language operator
proximal_lang_ray_trafo = odl.as_proximal_lang_operator(ray_trafo)
# Create sinogram of forward projected phantom with noise
phantom = odl.phantom.shepp_logan(reco_space, modified=True)
phantom.show('phantom')
data = ray_trafo(phantom)
data += odl.phantom.white_noise(ray_trafo.range) * np.mean(data) * 0.1
data.show('noisy data')
# Convert to array for ProxImaL
rhs_arr = data.asarray()
# Set up optimization problem
# Note that proximal is not aware of the underlying space and only works with
# matrices. Hence the norm in proximal does not match the norm in the ODL space
# exactly.