This class implements a regularized calibrationless reconstruction.

Parameters

fourier_op : object of class FFT, NonCartesianFFT or Stacked3DNFFT in

mri.operators

Defines the fourier operator F in the above equation.

linear_op : object, (optional, default None)

Defines the linear sparsifying operator W. This must operate on x and have 2 functions, op(x) and adj_op(coeff) which implements the operator and adjoint operator. For wavelets, this can be object of class WaveletN or WaveletUD2 from mri.operators . If None, sym8 wavelet with nb_scale=3 is chosen.

gradient_formulation : str between ‘analysis’ or ‘synthesis’,

default ‘synthesis’ defines the formulation of the image model which defines the gradient.

n_jobs : int, default 1

The number of cores to be used for faster reconstruction

verbose : int, optional default 0

Verbosity levels

1 => Print basic debug information 5 => Print all initialization information 20 => Calculate cost at the end of each iteration. 30 => Print the debug information of operators if defined by class NOTE - High verbosity (>20) levels are computationally intensive.

**kwargs : Extra keyword arguments

for gradient initialization:

Please refer to mri.operators.gradient.base for information

regularizer_op: operator, (optional default None)

Defines the regularization operator for the regularization function H. If None, the regularization chosen is Identity and the optimization turns to gradient descent.

Notes

For the Analysis case, finds the solution for x of: ..math:: (1/2) * sum(||F x_l - y_l||^2_2, n_coils) + mu * H(W x_l)

For the Synthesis case, finds the solution of: ..math:: (1/2) * sum(||F Wt alpha_l - y_l||^2_2, n_coils) + mu * H(alpha_l)