Gfft

template <typename T1> class Gfft

Uniform Cartesian FFT encoding operator.

Implements a fully sampled Cartesian Fourier encoding operator, wrapping FFTW on CPU, cuFFT on GPU (OpenACC path), or Apple vDSP/Accelerate (Metal path). This is the most efficient encoding operator for fully sampled Cartesian k-space trajectories.

Use G * x for the forward FFT and G / d for the adjoint (inverse FFT).

See : Gnufft for non-Cartesian (non-uniform) k-space trajectories.

Gfft<float> F(Nx, Ny, Nz);
Col<cx_float> kdata = F * image;  // forward FFT
Col<cx_float> recon = F / kdata;  // inverse FFT

T1 : Floating-point precision type (float or double).

Variables

Name	Description
stream	Image x-dimension in pixels.
plan	cuFFT plan handle.

Operators

Name	Description
operator*	Forward FFT: image -> k-space. d : Input image vector of length NxNyNz. Return : Output k-space vector of length NxNyNz.
operator/	Adjoint FFT (inverse FFT): k-space -> image. d : Input k-space vector of length NxNyNz. Return : Output image vector of length NxNyNz.
operator*	Forward FFT (forgeCol overload).
operator/	Adjoint FFT (forgeCol overload).

Functions

Name	Description
Gfft	Default constructor.
Gfft	Construct a Gfft operator for an Nx x Ny x Nz image grid.

Variable Details

plan

cufftHandle* plan

cuFFT plan handle.

stream

void* stream

Image x-dimension in pixels.
Image y-dimension in pixels.
Image z-dimension in pixels.
GPU stream handle (OpenACC/CUDA).

Operator Details

operator*

Col<CxT1> operator*(const Col<CxT1>& d) const

Forward FFT: image -> k-space.

d : Input image vector of length NxNyNz.

Return : Output k-space vector of length NxNyNz.

forgeCol<forgeComplex<T1>> operator*(const forgeCol<forgeComplex<T1>>& d) const

Forward FFT (forgeCol overload).

d : Input image vector of length NxNyNz.

Return : Output k-space vector of length NxNyNz.

operator/

Col<CxT1> operator/(const Col<CxT1>& d) const

Adjoint FFT (inverse FFT): k-space -> image.

d : Input k-space vector of length NxNyNz.

Return : Output image vector of length NxNyNz.

forgeCol<forgeComplex<T1>> operator/(const forgeCol<forgeComplex<T1>>& d) const

Adjoint FFT (forgeCol overload).

d : Input k-space vector of length NxNyNz.

Return : Output image vector of length NxNyNz.

Function Details

Gfft

Gfft()

Default constructor. Produces an uninitialized operator.

Gfft(uword ix, uword iy, uword iz)

Construct a Gfft operator for an Nx x Ny x Nz image grid.

ix : Image x-dimension in pixels (Nx).

iy : Image y-dimension in pixels (Ny).

iz : Image z-dimension in pixels (Nz); use 1 for 2-D.