mri.operators.gradient.gradient#

Classes for defining gradient operators.

class GradAnalysis(fourier_op, verbose=0, **kwargs)[source]#

Gradient class for analysis formulation.

This class defines the grad operators for: .. math:: frac{1}{2} sum_l ||F x - y_l||^2_2

Parameters

fourier_op (mri.operators.OperatorBase) – A Fourier operator such as FFT, NonCartesianFFT or Stacked3DNFFT, corresponding to F in the above equation.
verbose (int, default=0) – Verbose levels for debug prints. The default value is 0.

class GradSynthesis(fourier_op, linear_op, verbose=0, **kwargs)[source]#

Gradient class for synthesis formulation.

This class defines the grad operators for: .. math:: frac{1}{2} sum_l ||F Psi_t x - y_l||^2_2

Parameters

fourier_op (mri.operators.OperatorBase) – A Fourier operator such as FFT, NonCartesianFFT or Stacked3DNFFT, corresponding to F in the above equation.
linear_op (mri.operators.OperatorBase) – A linear operator such as WaveltN or WaveletUD2, corresponding to \(\Psi\) in above equation.
verbose (int, default=0) – Verbose levels for debug prints. The default value is 0.

class GradSelfCalibrationAnalysis(fourier_op, Smaps, verbose=0, **kwargs)[source]#

Gradient class for analysis formulation based on sensitivity profile.

This class defines the grad operators for: .. math:: frac{1}{2} sum_l ||F S_l x - y_l||^2_2

Parameters

fourier_op (mri.operators.OperatorBase) – A Fourier operator such as FFT, NonCartesianFFT or Stacked3DNFFT, corresponding to F in the above equation.
Smaps (numpy.ndarray) – The coil sensitivity profile of shape (L, *data.shape), composed of \(S_l\) in above equation.
verbose (int, default=0) – Verbose levels for debug prints. The default value is 0.

class GradSelfCalibrationSynthesis(fourier_op, linear_op, Smaps, verbose=0, **kwargs)[source]#

Gradient class for synthesis formulation based on sensitivity profile.

This class defines the grad operators for: .. math:: frac{1}{2} sum_l ||F S_l Psi_t x - y_l||^2_2

Parameters

fourier_op (mri.operators.OperatorBase) – A Fourier operator such as FFT, NonCartesianFFT or Stacked3DNFFT, corresponding to F in the above equation.
linear_op (mri.operators.OperatorBase) – A linear operator such as WaveltN or WaveletUD2, corresponding to \(\Psi\) in above equation.
Smaps (numpy.ndarray) – The coil sensitivity profile of shape (L, *data.shape), composed of \(S_l\) in above equation.
verbose (int, default=0) – Verbose levels for debug prints. The default value is 0.