NFFT: MRI - Transforms in magnetic resonance imaging

NFFT 3.4.1

Data Structures
struct	mri_inh_2d1d_plan

struct	mri_inh_3d_plan

Functions
void	mri_inh_2d1d_trafo (mri_inh_2d1d_plan *ths)

void	mri_inh_2d1d_init_guru (mri_inh_2d1d_plan ths, int N, int M, int *n, int m, double sigma, unsigned nfft_flags, unsigned fftw_flags)

void	mri_inh_2d1d_finalize (mri_inh_2d1d_plan *ths)

void	mri_inh_3d_trafo (mri_inh_3d_plan *ths)

void	mri_inh_3d_adjoint (mri_inh_3d_plan *ths)

void	mri_inh_3d_finalize (mri_inh_3d_plan *ths)

Detailed Description

Function Documentation

mri_inh_2d1d_trafo ( mri_inh_2d1d_plan * ths )

Executes a mri transformation considering the field inhomogeneity with the 2d1d method, i.e. computes for $j=0,...,M_{total}-1$

$f(x_j) = \sum_{k \in I_N^2} \hat{f}(k) {\rm e}^{\mbox{\rm\scriptsize i} t_j \omega(k)} {\rm e}^{-2 \pi \mbox{\rm\scriptsize i} k x_j}$

ths_plan The plan

Author: Tobias Knopp

Definition at line 57 of file mri.c.

References nfft_plan::f, mri_inh_2d1d_plan::f, nfft_plan::f_hat, mri_inh_2d1d_plan::f_hat, nfft_plan::m, mri_inh_2d1d_plan::M_total, mri_inh_2d1d_plan::N_total, nfft_free(), nfft_malloc(), and nfft_trafo().

Referenced by construct(), and mri_inh_2d1d_init_guru().

void mri_inh_2d1d_init_guru	(	mri_inh_2d1d_plan *	ths,
		int *	N,
		int	M,
		int *	n,
		int	m,
		double	sigma,
		unsigned	nfft_flags,
		unsigned	fftw_flags
	)

Creates a transform plan.

ths_plan The plan for the transform
N The bandwidth
M_total The number of nodes
n The oversampled bandwidth
m The cut-off parameter
sigma The oversampling factor
nnfft_flags The flags

Author: Tobias Knopp

Definition at line 156 of file mri.c.

References nfft_plan::f, mri_inh_2d1d_plan::f, nfft_plan::f_hat, mri_inh_2d1d_plan::f_hat, nfft_plan::M_total, mri_inh_2d1d_plan::M_total, mri_inh_2d1d_trafo(), mri_inh_2d1d_plan::mv_adjoint, mri_inh_2d1d_plan::mv_trafo, nfft_plan::N_total, mri_inh_2d1d_plan::N_total, and nfft_malloc().

Referenced by construct().

mri_inh_2d1d_finalize ( mri_inh_2d1d_plan * ths )

Destroys a plan.

ths_plan The plan

Author: Tobias Knopp

Definition at line 174 of file mri.c.

References nfft_plan::f, mri_inh_2d1d_plan::f, nfft_plan::f_hat, mri_inh_2d1d_plan::f_hat, nfft_finalize(), and nfft_free().

Referenced by construct().

mri_inh_3d_trafo ( mri_inh_3d_plan * ths )

Executes a mri transformation considering the field inhomogeneity with the 3d method, i.e. computes for $j=0,...,M_{total}-1$

$f(x_j) = \sum_{k \in I_N^2} \hat{f}(k) {\rm e}^{\mbox{\rm\scriptsize i} t_j \omega(k)} {\rm e}^{-2 \pi \mbox{\rm\scriptsize i} k x_j}$

ths_plan The plan

Author: Tobias Knopp

Definition at line 189 of file mri.c.

References nfft_plan::f, mri_inh_3d_plan::f, nfft_plan::f_hat, mri_inh_3d_plan::f_hat, nfft_plan::m, mri_inh_3d_plan::M_total, mri_inh_3d_plan::N_total, nfft_free(), nfft_malloc(), nfft_trafo(), and nfft_plan::x.

Referenced by construct().

mri_inh_3d_adjoint ( mri_inh_3d_plan * ths )

Executes an adjoint mri transformation considering the field inhomogeneity with the 3d method, i.e. computes for $k \in I_N^2$

$\hat{f}(k) = \sum_{j=0}^{M_{total}-1} f(x_j) {\rm e}^{\mbox{\rm\scriptsize i} t_j \omega(k)} {\rm e}^{-2 \pi \mbox{\rm\scriptsize i} k x_j}$

ths_plan The plan

Author: Tobias Knopp

Definition at line 221 of file mri.c.

References nfft_plan::f, mri_inh_3d_plan::f, nfft_plan::f_hat, mri_inh_3d_plan::f_hat, nfft_plan::m, mri_inh_3d_plan::M_total, mri_inh_3d_plan::N_total, nfft_adjoint(), nfft_free(), nfft_malloc(), and nfft_plan::x.

mri_inh_3d_finalize ( mri_inh_3d_plan * ths )

Destroys a plan.

ths_plan The plan

Author: Tobias Knopp

Definition at line 266 of file mri.c.

References mri_inh_3d_plan::f_hat, nfft_finalize(), and nfft_free().

Referenced by construct().