3.0 API Reference

MRI - Transforms in magnetic resonance imaging


Data Structures
struct	mri_inh_2d1d_plan
	The structure for the transform plan. More...
struct	mri_inh_3d_plan
	The structure for the transform plan. More...
Functions
void	mri_inh_2d1d_trafo (mri_inh_2d1d_plan *ths)
	Executes a mri transformation considering the field inhomogeneity with the 2d1d method, i.e.
void	mri_inh_2d1d_adjoint (mri_inh_2d1d_plan *ths)
	Executes an adjoint mri transformation considering the field inhomogeneity with the 2d1d method, i.e.
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.
void	mri_inh_2d1d_finalize (mri_inh_2d1d_plan *ths)
	Destroys a plan.
void	mri_inh_3d_trafo (mri_inh_3d_plan *ths)
	Executes a mri transformation considering the field inhomogeneity with the 3d method, i.e.
void	mri_inh_3d_adjoint (mri_inh_3d_plan *ths)
	Executes an adjoint mri transformation considering the field inhomogeneity with the 3d method, i.e.
void	mri_inh_3d_init_guru (mri_inh_3d_plan ths, int N, int M, int *n, int m, double sigma, unsigned nfft_flags, unsigned fftw_flags)
void	mri_inh_3d_finalize (mri_inh_3d_plan *ths)
	Destroys a plan.

Function Documentation

void 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 40 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, window_funct_plan_::n, mri_inh_2d1d_plan::N3, mri_inh_2d1d_plan::N_total, nfft_trafo(), PI, mri_inh_2d1d_plan::plan, mri_inh_2d1d_plan::sigma3, mri_inh_2d1d_plan::t, and mri_inh_2d1d_plan::w.
Referenced by construct().

void mri_inh_2d1d_adjoint ( mri_inh_2d1d_plan * ths )

Executes an adjoint mri transformation considering the field inhomogeneity with the 2d1d 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 82 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, window_funct_plan_::n, mri_inh_2d1d_plan::N3, mri_inh_2d1d_plan::N_total, nfft_adjoint(), PI, mri_inh_2d1d_plan::plan, mri_inh_2d1d_plan::sigma3, mri_inh_2d1d_plan::t, and mri_inh_2d1d_plan::w.

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 $N$

M_total The number of nodes $x$

n The oversampled bandwidth $N$

m The cut-off parameter

sigma The oversampling factor

nnfft_flags The flags

Author:
Tobias Knopp

Definition at line 134 of file mri.c.
References mri_inh_2d1d_plan::f, nfft_plan::f, mri_inh_2d1d_plan::f_hat, nfft_plan::f_hat, mri_inh_2d1d_plan::M_total, nfft_plan::M_total, mri_inh_2d1d_plan::N3, mri_inh_2d1d_plan::N_total, nfft_plan::N_total, nfft_init_guru(), mri_inh_2d1d_plan::plan, mri_inh_2d1d_plan::sigma3, mri_inh_2d1d_plan::t, and mri_inh_2d1d_plan::w.
Referenced by construct(), and reconstruct().

void 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 164 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, window_funct_plan_::m, mri_inh_3d_plan::M_total, window_funct_plan_::n, mri_inh_3d_plan::N3, mri_inh_3d_plan::N_total, nfft_trafo(), mri_inh_3d_plan::plan, mri_inh_3d_plan::sigma3, mri_inh_3d_plan::w, and nfft_plan::x.
Referenced by construct().

void 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 196 of file mri.c.
References nfft_plan::f, mri_inh_3d_plan::f, mri_inh_3d_plan::f_hat, nfft_plan::f_hat, nfft_plan::m, window_funct_plan_::m, mri_inh_3d_plan::M_total, window_funct_plan_::n, mri_inh_3d_plan::N3, mri_inh_3d_plan::N_total, nfft_adjoint(), mri_inh_3d_plan::plan, mri_inh_3d_plan::sigma3, mri_inh_3d_plan::w, and nfft_plan::x.

void mri_inh_3d_finalize ( mri_inh_3d_plan * ths )

Destroys a plan.

ths_plan The plan

Author:
Tobias Knopp

Definition at line 238 of file mri.c.
References mri_inh_3d_plan::f_hat, nfft_finalize(), mri_inh_3d_plan::plan, and mri_inh_3d_plan::w.
Referenced by construct(), and reconstruct().

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