3.0 API Reference

radon.c File Reference

NFFT-based discrete Radon transform. More...

#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <string.h>
#include "util.h"
#include "nfft3.h"

Go to the source code of this file.

Defines

#define KERNEL(r) (1.0-fabs((double)(r))/((double)R/2))

define weights of kernel function for discrete Radon transform

Functions

int polar_grid (int T, int R, double *x, double *w)

generates the points x with weights w for the polar grid with T angles and R offsets

int linogram_grid (int T, int R, double *x, double *w)

generates the points x with weights w for the linogram grid with T slopes and R offsets

int Radon_trafo (int(*gridfcn)(), int T, int R, double *f, int NN, double *Rf)

computes the NFFT-based discrete Radon transform of f on the grid given by gridfcn() with T angles and R offsets

int main (int argc, char **argv)

simple test program for the discrete Radon transform

Detailed Description

NFFT-based discrete Radon transform.

Computes the discrete Radon transform

$R_{\theta_t} f\left(\frac{s}{R}\right) = \sum_{r \in I_R} w_r \; \sum_{k \in I_N^2} f_{k} \mathrm{e}^{-2\pi\mathrm{I} k \; (\frac{r}{R}\theta_t)} \, \mathrm{e}^{2\pi\mathrm{i} r s / R} \qquad(t \in I_T, s \in I_R).$

by taking the 2D-NFFT of $f_k$ ( $k \in I_N^2$ ) at the points $\frac{r}{R}\theta_t$ of the polar or linogram grid followed by 1D-iFFTs for every direction $t \in T$ , where $w_r$ are the weights of the Dirichlet- or Fejer-kernel.

Author:: Markus Fenn

Date:: 2005

Definition in file radon.c.

Function Documentation

int Radon_trafo ( int(*)() gridfcn,

int T,

int R,

double * f,

int NN,

double * Rf

)

computes the NFFT-based discrete Radon transform of f on the grid given by gridfcn() with T angles and R offsets
< index for nodes and freqencies
< plan for the nfft-2D
< variable for the fftw-1Ds
< plan for the fftw-1Ds
< index for directions and offsets
< knots and associated weights
init two dimensional NFFT plan
init nodes from grid
precompute psi, the entries of the matrix B
init Fourier coefficients from given image
NFFT-2D
FFTW-1Ds
finalise the plans and free the variables
Definition at line 91 of file radon.c.
References nfft_plan::f, nfft_plan::f_hat, fft(), FFT_OUT_OF_PLACE, FFTW_INIT, KERNEL, nfft_plan::M_total, MALLOC_F, MALLOC_F_HAT, MALLOC_X, nfft_plan::N_total, nfft_fftshift_complex(), nfft_finalize(), nfft_plan::nfft_flags, nfft_init_guru(), nfft_precompute_full_psi(), nfft_precompute_lin_psi(), nfft_precompute_psi(), nfft_trafo(), PRE_FULL_PSI, PRE_LIN_PSI, PRE_PHI_HUT, PRE_PSI, and nfft_plan::x.
Referenced by main().

int main ( int argc,

char ** argv

)

simple test program for the discrete Radon transform
< grid generating function
< number of directions/offsets
< image size
load data
Radon transform
write result
free the variables
Definition at line 182 of file radon.c.
References linogram_grid(), polar_grid(), and Radon_trafo().

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Defines
#define	KERNEL(r) (1.0-fabs((double)(r))/((double)R/2))
	define weights of kernel function for discrete Radon transform
Functions
int	polar_grid (int T, int R, double x, double w)
	generates the points x with weights w for the polar grid with T angles and R offsets
int	linogram_grid (int T, int R, double x, double w)
	generates the points x with weights w for the linogram grid with T slopes and R offsets
int	Radon_trafo (int(gridfcn)(), int T, int R, double f, int NN, double *Rf)
	computes the NFFT-based discrete Radon transform of f on the grid given by gridfcn() with T angles and R offsets
int	main (int argc, char **argv)
	simple test program for the discrete Radon transform