# #############################################################################
# pySAP - Copyright (C) CEA, 2017 - 2018 #
# Distributed under the terms of the CeCILL-B license, #
# as published by the CEA-CNRS-INRIA. Refer to the LICENSE file or to #
# http://www.cecill.info/licences/Licence_CeCILL-B_V1-en.html for details. #
# #############################################################################
"""Classes for defining gradient operators."""
# Internal import
from .base import GradBaseMRI
from ..fourier.utils import check_if_fourier_op_uses_sense
# Third party import
import numpy as np
[docs]class GradAnalysis(GradBaseMRI):
r"""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.
"""
def __init__(self, fourier_op, verbose=0, **kwargs):
if fourier_op.n_coils != 1 and not check_if_fourier_op_uses_sense(fourier_op):
data_shape = (fourier_op.n_coils, *fourier_op.shape)
else:
data_shape = fourier_op.shape
super(GradAnalysis, self).__init__(
operator=fourier_op.op,
trans_operator=fourier_op.adj_op,
shape=data_shape,
verbose=verbose,
**kwargs,
)
self.fourier_op = fourier_op
[docs]class GradSynthesis(GradBaseMRI):
r"""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 :math:`\Psi` in above equation.
verbose: int, default=0
Verbose levels for debug prints. The default value is 0.
"""
def __init__(self, fourier_op, linear_op, verbose=0, **kwargs):
self.fourier_op = fourier_op
self.linear_op = linear_op
coef = linear_op.op(np.squeeze(np.zeros((linear_op.n_coils,
*fourier_op.shape))))
self.linear_op_coeffs_shape = coef.shape
super(GradSynthesis, self).__init__(
self._op_method,
self._trans_op_method,
self.linear_op_coeffs_shape,
verbose=verbose,
**kwargs,
)
[docs] def _op_method(self, data):
return self.fourier_op.op(self.linear_op.adj_op(data))
[docs] def _trans_op_method(self, data):
return self.linear_op.op(self.fourier_op.adj_op(data))
[docs]class GradSelfCalibrationAnalysis(GradBaseMRI):
r"""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 :math:`S_l` in above equation.
verbose: int, default=0
Verbose levels for debug prints. The default value is 0.
"""
def __init__(self, fourier_op, Smaps, verbose=0, **kwargs):
self.Smaps = Smaps
self.fourier_op = fourier_op
super(GradSelfCalibrationAnalysis, self).__init__(
self._op_method,
self._trans_op_method,
fourier_op.shape,
verbose=verbose,
**kwargs,
)
[docs] def _op_method(self, data):
data_per_ch = data * self.Smaps
return self.fourier_op.op(data_per_ch)
[docs] def _trans_op_method(self, coeff):
data_per_ch = self.fourier_op.adj_op(coeff)
return np.sum(data_per_ch * np.conjugate(self.Smaps), axis=0)
[docs]class GradSelfCalibrationSynthesis(GradBaseMRI):
r"""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 :math:`\Psi` in above equation.
Smaps: numpy.ndarray
The coil sensitivity profile of shape (L, *data.shape),
composed of :math:`S_l` in above equation.
verbose: int, default=0
Verbose levels for debug prints. The default value is 0.
"""
def __init__(self, fourier_op, linear_op, Smaps, verbose=0,
**kwargs):
self.Smaps = Smaps
self.fourier_op = fourier_op
self.linear_op = linear_op
coef = linear_op.op(np.zeros(fourier_op.shape))
self.linear_op_coeffs_shape = coef.shape
super(GradSelfCalibrationSynthesis, self).__init__(
self._op_method,
self._trans_op_method,
self.linear_op_coeffs_shape,
verbose=verbose,
**kwargs,
)
[docs] def _op_method(self, coeff):
image = self.linear_op.adj_op(coeff)
image_per_ch = image * self.Smaps
return self.fourier_op.op(image_per_ch)
[docs] def _trans_op_method(self, data):
data_per_ch = self.fourier_op.adj_op(data)
image_recon = np.sum(data_per_ch * np.conjugate(self.Smaps), axis=0)
return self.linear_op.op(image_recon)
