Python Sparse data Analysis Package external MRI plugin.

This module defines primal dual optimizers

mri.optimizers.primal_dual.condatvu(gradient_op, linear_op, dual_regularizer, cost_op, max_nb_of_iter=150, tau=None, sigma=None, relaxation_factor=1.0, x_init=None, std_est=None, std_est_method=None, std_thr=2.0, nb_of_reweights=1, metric_call_period=5, metrics={}, verbose=0)[source]¶

The Condat-Vu sparse reconstruction with reweightings.

Parameters

gradient_op: instance of class GradBase

the gradient operator.

linear_op: instance of LinearBase

the linear operator: seek the sparsity, ie. a wavelet transform.

dual_regularizer: instance of ProximityParent

the dual regularization operator

cost_op: instance of costObj

the cost function used to check for convergence during the optimization.

max_nb_of_iter: int, default 150

the maximum number of iterations in the Condat-Vu proximal-dual splitting algorithm.

tau, sigma: float, default None

parameters of the Condat-Vu proximal-dual splitting algorithm. If None estimates these parameters.

relaxation_factor: float, default 0.5

parameter of the Condat-Vu proximal-dual splitting algorithm. If 1, no relaxation.

x_init: np.ndarray (optional, default None)

the initial guess of image

std_est: float, default None

the noise std estimate. If None use the MAD as a consistent estimator for the std.

std_est_method: str, default None

if the standard deviation is not set, estimate this parameter using the mad routine in the image (‘primal’) or in the sparse wavelet decomposition (‘dual’) domain.

std_thr: float, default 2.

use this treshold expressed as a number of sigma in the residual proximity operator during the thresholding.

relaxation_factor: float, default 0.5

parameter of the Condat-Vu proximal-dual splitting algorithm. If 1, no relaxation.

nb_of_reweights: int, default 1

the number of reweightings.

metric_call_period: int (default 5)

the period on which the metrics are compute.

metrics: dict (optional, default None)

the list of desired convergence metrics: {‘metric_name’: [@metric, metric_parameter]}. See modopt for the metrics API.

verbose: int, default 0

the verbosity level.

Returns

x_final: ndarray

the estimated CONDAT-VU solution.

costs: list of float

the cost function values.

metrics: dict

the requested metrics values during the optimization.

y_final: ndarrat

the estimated dual CONDAT-VU solution