def testTotalVariation():
im = scipy.misc.ascent()
im = im[:, :, np.newaxis].astype(np.uint8)
fn = proximal.norm1(proximal.grad(proximal.Variable(im.shape)))
thresh = 6
out = fn.prox(thresh, im)
def solver(f, kernel_img, metric, cnn_func, elemental):
"""
Solves the deblurring problem for the given input and kernel image.
:param f: Corrupted input image
:type f: np.ndarray
:param kernel_img: Blur kernel
:type kernel_img: np.ndarray
:param metric: Preinitialized metric
:type metric: proximal.utils.metrics
:param cnn_func: Preinitialized deployment CNN
:type cnn_func: function
:param elemental: General experiment configuration parameters
:type elemental: Dict
:returns: Reconstructed output image
:rtype: np.ndarray
"""
# pylint:disable=no-value-for-parameter
options = px.cg_options(tol=1e-4, num_iters=100, verbose=True)
u = px.Variable(f.shape)
alpha_sumsquare = elemental['alpha_data'] / 2.0
A_u = px.conv(kernel_img, u)
prox_fns = px.sum_squares(A_u - f, alpha=alpha_sumsquare)
if elemental['alpha_tv'] > 0.0:
prox_fns += px.norm1(elemental['alpha_tv'] * px.grad(u))
prox_fns += init_denoising_prior(u,
cnn_func,
sigma=elemental['sigma'],
sigma_scale=elemental['sigma_scale'])
prob = init_problem(prox_fns)
solve_problem(prob,
x0=f.copy(),
metric=metric,
sigma=elemental['sigma'],
lin_solver_options=options)
return np.clip(u.value, 0.0, 1.0)
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)
result_odl.show('result from ProxImaL')
# 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)
result_odl.show('result from ProxImaL')
def solver(f, x0, metric, cnn_func, elemental):
"""
Solves the demosaicking problem for the given input.
:param f: Corrupted input image
:type f: np.ndarray
:param x0: Predemosaicked initialization image
:type x0: np.ndarray
:param metric: Preinitialized metric
:type metric: proximal.utils.metrics
:param cnn_func: Preinitialized deployment CNN
:type cnn_func: function
:param elemental: General experiment configuration parameters
:type elemental: Dict
:returns: Reconstructed output image
:rtype: np.ndarray
"""
# pylint:disable=no-value-for-parameter
options = px.cg_options(tol=1e-4, num_iters=100, verbose=True)
u = px.Variable(f.shape)
A = bayer_mask(f.shape)
A_u = px.mul_elemwise(A, u)
alpha_sumsquare = elemental['alpha_data'] / 2.0
data = px.sum_squares(A_u - f, alpha=alpha_sumsquare)
prox_fns = data
if elemental['alpha_tv'] > 0.0:
prox_fns += px.norm1(elemental['alpha_tv'] * px.grad(u, dims=2))
if elemental['alpha_cross'] > 0.0:
grad_u = px.grad(u, dims=2)
grad_x0 = px.grad(x0, dims=2).value
x0_stacked = np.array([x0, x0]).reshape(x0.shape + (2, ))
u_stacked = px.reshape(px.hstack([u, u]), x0.shape + (2, ))
cross_1 = px.vstack([
px.mul_elemwise(np.roll(x0_stacked, 1, 2), grad_u),
px.mul_elemwise(np.roll(x0_stacked, 2, 2), grad_u)
])
cross_2 = px.vstack([
px.mul_elemwise(np.roll(grad_x0, 1, 2), u_stacked),
px.mul_elemwise(np.roll(grad_x0, 2, 2), u_stacked)
])
prox_fns += px.norm1(0.5 * elemental['alpha_cross'] *
(cross_1 - cross_2))
prox_fns += init_denoising_prior(u,
cnn_func,
sigma=elemental['sigma'],
sigma_scale=elemental['sigma_scale'])
prob = init_problem(prox_fns)
solve_problem(prob,
x0=x0,
metric=metric,
sigma=elemental['sigma'],
lin_solver_options=options)
return np.clip(u.value, 0.0, 1.0)
# 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.
x = proximal.Variable(reco_space.shape)
funcs = [proximal.sum_squares(proximal_lang_ray_trafo(x) - rhs_arr),
0.2 * proximal.norm1(proximal.grad(x)),
proximal.nonneg(x),
proximal.nonneg(1 - x)]
# Solve the problem using ProxImaL
prob = proximal.Problem(funcs)
prob.solve(verbose=True)
# Convert back to odl and display result
result_odl = reco_space.element(x.value)
result_odl.show('ProxImaL result')