def test_reconstruction_condat_vu_fft2(self):
""" Test all the registered transformations.
"""
print("Process test FFT2 Condat Vu algorithm::")
for image in self.images:
fourier = FFT2(samples=convert_mask_to_locations(
fftshift(self.mask)),
shape=image.shape)
data = fourier.op(image.data)
fourier_op = FFT2(convert_mask_to_locations(fftshift(self.mask)),
shape=image.shape)
print("Process test with image '{0}'...".format(
image.metadata["path"]))
for nb_scale in self.nb_scales:
print("- Number of scales: {0}".format(nb_scale))
for name in self.names:
print(" Transform: {0}".format(name))
linear_op = WaveletN(wavelet_name=name, nb_scale=4)
gradient_op = GradAnalysis2(data=data,
fourier_op=fourier_op)
prox_dual_op = Threshold(0)
x_final, transform, _, _ = sparse_rec_condatvu(
gradient_op=gradient_op,
linear_op=linear_op,
prox_dual_op=prox_dual_op,
cost_op=None,
std_est=0.0,
std_est_method="dual",
std_thr=0,
tau=None,
sigma=None,
relaxation_factor=1.0,
nb_of_reweights=0,
max_nb_of_iter=self.nb_iter,
add_positivity=False,
atol=1e-4,
verbose=0)
fourier_0 = FFT2(samples=convert_mask_to_locations(
fftshift(self.mask)),
shape=image.shape)
data_0 = fourier_0.op(numpy.fft.fftshift(image.data))
self.assertTrue(
numpy.allclose(x_final.any(),
numpy.fft.ifftshift(
fourier_0.adj_op(data_0)).any(),
rtol=1e-10))
mean_square_error = numpy.mean(
numpy.abs(
x_final -
numpy.fft.ifftshift(fourier_0.adj_op(data_0)))**2)
print(" Mean Square Error = ", mean_square_error)
return
wavelet_name="BsplineWaveletTransformATrousAlgorithm",
samples=kspace_loc,
nb_scales=4,
non_cartesian=True,
uniform_data_shape=image.shape,
gradient_space="analysis")
# Start the CONDAT-VU reconstruction
max_iter = 20
x_final, transform, costs, metrics = sparse_rec_condatvu(
gradient_op,
linear_op,
prox_op,
cost_op,
std_est=None,
std_est_method="dual",
std_thr=2.,
mu=1e-9,
tau=None,
sigma=None,
relaxation_factor=1.0,
nb_of_reweights=2,
max_nb_of_iter=max_iter,
add_positivity=False,
atol=1e-4,
verbose=1)
image_rec = pysap.Image(data=np.abs(x_final))
image_rec.show()
cost_rec = pysap.Image(data=costs)
cost_rec.show()
#
# We now want to refine the zero order solution using a Condat-Vu
# optimization.
# We can't use a FISTA optimisation, which is adapted to solve the synthesis
# formulation of a Lasso.
# But here, we need to use the analysis formulation since the learnt
# dictionary is not a basis anymore. It is redundant.
x, y, costs, metrics = sparse_rec_condatvu(gradient_op=gradient_op,
linear_op=linear_op,
prox_dual_op=prox_dual_op,
cost_op=cost_op,
std_est=None,
std_est_method=None,
std_thr=2.,
mu=0.1,
tau=None,
sigma=None,
relaxation_factor=1.0,
nb_of_reweights=0,
max_nb_of_iter=2,
add_positivity=False,
atol=1e-4,
verbose=1)
#############################################################################
# Visualizing the results
# -----------------------
# Solution in the image domain
image_rec = pysap.Image(data=min_max_normalize(np.abs(x)))
image_rec.show()