mri.operators.fourier.cartesian

Fourier operators for Cartesian sampling in k-space.

class FFT(shape, n_coils=1, samples=None, mask=None, n_jobs=1)

Bases: mri.operators.fourier.base.FourierOperatorBase

Standard unitary ND Fast Fourier Transform (FFT) class.

The FFT will be normalized in a symmetric way. Here, ND = 2D or 3D.

samples

the mask samples, i.e. measurements in the Fourier domain.

Type

numpy.ndarray

shape

shape of the image (not necessarly a square matrix).

Type

tuple of int

n_coils

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]

Type

int, default 1

n_jobs

Number of parallel workers to use for Fourier computation

Type

int, default 1

op(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 – masked Fourier transform of the input image. For multicoil images the coils dimension is put first.

Return type

numpy.ndarray

adj_op(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 – inverse ND discrete Fourier transform of the input coefficients. For multicoil images the coils dimension is put first.

Return type

numpy.ndarray