NFFT-based discrete Radon transform. More...

#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <complex.h>
#include "nfft3mp.h"

Include dependency graph for radon.c:

Go to the source code of this file.

Macros
#define	NFFT_PRECISION_DOUBLE

#define	KERNEL(r) (NFFT_K(1.0)-NFFT_M(fabs)((NFFT_R)(r))/((NFFT_R)S/2))
	define weights of kernel function for discrete Radon transform

Functions
static int	polar_grid (int T, int S, NFFT_R x, NFFT_R w)
	generates the points x with weights w for the polar grid with T angles and R offsets

static int	linogram_grid (int T, int S, NFFT_R x, NFFT_R w)
	generates the points x with weights w for the linogram grid with T slopes and R offsets

static int	Radon_trafo (int(gridfcn)(int T, int S, NFFT_R x, NFFT_R w), int T, int S, NFFT_R f, int NN, NFFT_R *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 ( $k \in I_N^2$ ) 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 are the weights of the Dirichlet- or Fejer-kernel.