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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 60 of file mri.c.

References mri_inh_2d1d_plan::f, nfft_plan::f, mri_inh_2d1d_plan::f_hat, nfft_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_free(), nfft_malloc(), 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(), and mri_inh_2d1d_init_guru().

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 102 of file mri.c.

References mri_inh_2d1d_plan::f, nfft_plan::f, mri_inh_2d1d_plan::f_hat, nfft_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(), nfft_free(), nfft_malloc(), PI, mri_inh_2d1d_plan::plan, mri_inh_2d1d_plan::sigma3, mri_inh_2d1d_plan::t, and mri_inh_2d1d_plan::w.

Referenced by 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 $N$
  • 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 154 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_adjoint(), mri_inh_2d1d_trafo(), mri_inh_2d1d_plan::mv_adjoint, mri_inh_2d1d_plan::mv_trafo, mri_inh_2d1d_plan::N3, nfft_plan::N_total, mri_inh_2d1d_plan::N_total, nfft_init_guru(), nfft_malloc(), 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_finalize ( mri_inh_2d1d_plan ths  ) 

Destroys a plan.

  • ths_plan The plan
Author:
Tobias Knopp

Definition at line 172 of file mri.c.

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

Referenced by construct().

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 187 of file mri.c.

References mri_inh_3d_plan::f, nfft_plan::f, mri_inh_3d_plan::f_hat, nfft_plan::f_hat, window_funct_plan_::m, nfft_plan::m, mri_inh_3d_plan::M_total, window_funct_plan_::n, mri_inh_3d_plan::N3, mri_inh_3d_plan::N_total, nfft_free(), nfft_malloc(), 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 219 of file mri.c.

References mri_inh_3d_plan::f, nfft_plan::f, nfft_plan::f_hat, mri_inh_3d_plan::f_hat, window_funct_plan_::m, nfft_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(), nfft_free(), nfft_malloc(), 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 264 of file mri.c.

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

Referenced by construct().


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