mri.reconstructors.single_channel#

Single channel reconstruction.

class SingleChannelReconstructor(fourier_op, linear_op=None, gradient_formulation='synthesis', verbose=0, **kwargs)[source]#

Bases: mri.reconstructors.base.ReconstructorBase

Single channel MR image Reconstruction.

Notes

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

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

with ..math:: alpha = W x and x = Wt alpha

Parameters

fourier_op (Instance of OperatorBase.) – Defines the fourier operator F in the above equation.
linear_op (OperatorBase, default None) – Defines the linear sparsifying operator denoted \(W\) in the equation above. 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.linear If None, sym8 wavelet with nb_scale=3 is chosen.
regularizer_op (operator, (optional default None)) – Defines the regularization operator for the regularization function denoted \(H\) in the equation above. If None, the regularization chosen is Identity and the optimization turns to gradient descent.
gradient_formulation (str between 'analysis' or 'synthesis',) – default ‘synthesis’ defines the formulation of the image model which defines the gradient.
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.