NFFT-based discrete inverse Radon transform. More...

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

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	inverse_radon_trafo (int(gridfcn)(), int T, int S, NFFT_R Rf, int NN, NFFT_R *f, int max_i)
	computes the inverse discrete Radon transform of Rf on the grid given by gridfcn() with T angles and R offsets by a NFFT-based CG-type algorithm

int	main (int argc, char **argv)
	simple test program for the inverse discrete Radon transform

Detailed Description

NFFT-based discrete inverse Radon transform.

Computes the inverse of the discrete Radon transform

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

given at the points $\frac{r}{R}\theta_t$ of the polar or linogram grid and where $w_r$ are the weights of the Dirichlet- or Fejer-kernel by 1D-FFTs and the 2D-iNFFT.

Author: Markus Fenn

Date: 2005

Definition in file inverse_radon.c.

Macros

Functions

Detailed Description