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3.2.3 |
NFFT-based discrete Radon transform. More...
#include "config.h"#include <stdio.h>#include <math.h>#include <stdlib.h>#include <string.h>#include "nfft3util.h"#include "nfft3.h"Go to the source code of this file.
Macros | |
| #define | KERNEL(r) (1.0-fabs((double)(r))/((double)R/2)) |
| define weights of kernel function for discrete Radon transform | |
Functions | |
| static 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 | |
| static 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 | |
NFFT-based discrete Radon transform.
Computes the discrete Radon transform
![\[ R_{\theta_t} f\left(\frac{s}{R}\right) = \sum_{r \in I_R} w_r \; \sum_{k \in I_N^2} f_{k} \mathrm{e}^{-2\pi\mathrm{I} k \; (\frac{r}{R}\theta_t)} \, \mathrm{e}^{2\pi\mathrm{i} r s / R} \qquad(t \in I_T, s \in I_R). \]](form_134.png)
by taking the 2D-NFFT of 
( 
) at the points 
of the polar or linogram grid followed by 1D-iFFTs for every direction 
, where 
are the weights of the Dirichlet- or Fejer-kernel.
Definition in file radon.c.