# -*- coding: utf-8 -*-
##########################################################################
# 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.
##########################################################################
"""
Fourier operators for Cartesian sampling in k-space.
"""
# System import
import warnings
import numpy as np
import scipy as sp
# Package import
from .base import FourierOperatorBase
from .utils import convert_locations_to_mask, convert_mask_to_locations
from modopt.interface.errors import warn
[docs]class FFT(FourierOperatorBase):
"""Standard unitary ND Fast Fourier Transform (FFT) class.
The FFT will be normalized in a symmetric way. Here, ND = 2D or 3D.
Attributes
----------
samples: numpy.ndarray
the mask samples, i.e. measurements in the Fourier domain.
shape: tuple of int
shape of the image (not necessarly a square matrix).
n_coils: int, default 1
Number of coils used to acquire the signal in case of multicoil
acquisition. If n_coils > 1, data shape must be
[n_coils, Nx, Ny, Nz]
n_jobs: int, default 1
Number of parallel workers to use for Fourier computation
"""
def __init__(self, shape, n_coils=1, samples=None, mask=None, n_jobs=1):
"""Initialize the `FFT` class.
Parameters
----------
shape: tuple of int
shape of the image (not necessarly a square matrix).
n_coils: int, default 1
Number of coils used to acquire the signal in case of
multicoil acquisition. If n_coils > 1,
data shape must be equal to [n_coils, Nx, Ny, Nz]
samples: numpy.ndarray, default None
the mask samples in the Fourier domain.
mask: numpy.ndarray, default None
the mask as a matrix with 1 at sample locations
please pass samples or mask
n_jobs: int, default 1
Number of parallel workers to use for Fourier computation
All cores are used if -1
"""
self.shape = shape
if mask is None and samples is None:
raise ValueError("Please pass either samples or mask as input")
if mask is None:
self.mask = convert_locations_to_mask(samples, self.shape)
self.samples = samples
else:
self.mask = mask
self.samples = convert_mask_to_locations(mask)
if n_coils <= 0:
warn("The number of coils should be strictly positive")
n_coils = 1
self.n_coils = n_coils
self.n_jobs = n_jobs
[docs] def op(self, img):
"""This method calculates the masked Fourier transform of a ND image.
Parameters
----------
img: numpy.ndarray
input ND array with the same shape as the mask. For multicoil
images the coil dimension is put first.
Returns
-------
x: numpy.ndarray
masked Fourier transform of the input image. For multicoil
images the coils dimension is put first.
"""
if self.n_coils == 1:
return self.mask * sp.fft.ifftshift(sp.fft.fftn(
sp.fft.fftshift(img),
norm="ortho",
workers=self.n_jobs,
))
else:
if self.n_coils > 1 and self.n_coils != img.shape[0]:
raise ValueError("The number of coils parameter is not equal"
"to the actual number of coils, the data must"
"be reshaped as [n_coils, Nx, Ny, Nz]")
else:
axes = tuple(np.arange(1, img.ndim))
return self.mask * sp.fft.ifftshift(
sp.fft.fftn(
sp.fft.fftshift(
img,
axes=axes
),
axes=axes,
norm="ortho",
workers=self.n_jobs,
),
axes=axes
)
[docs] def adj_op(self, x):
"""Compute the inverse masked Fourier transform of a ND
image.
Parameters
----------
x: numpy.ndarray
masked Fourier transform data. For multicoil
images the coils dimension is put first.
Returns
-------
img: numpy.ndarray
inverse ND discrete Fourier transform of the input coefficients.
For multicoil images the coils dimension is put first.
"""
if self.n_coils == 1:
return sp.fft.fftshift(sp.fft.ifftn(
sp.fft.ifftshift(self.mask * x),
norm="ortho",
workers=self.n_jobs,
))
else:
if self.n_coils > 1 and self.n_coils != x.shape[0]:
raise ValueError("The number of coils parameter is not equal"
"to the actual number of coils, the data must"
"be reshaped as [n_coils, Nx, Ny, Nz]")
else:
x = x * self.mask
axes = tuple(np.arange(1, x.ndim))
return sp.fft.fftshift(
sp.fft.ifftn(
sp.fft.ifftshift(
x,
axes=axes
),
axes=axes,
norm="ortho",
workers=self.n_jobs,
),
axes=axes
)
