![\[ R_{\theta_t} f\left(\frac{s}{R}\right) = \sum_{r \in I_R} w_r \; \sum_{k \in I_N^2} f_{k} \mathrm{e}^{-2\pi\mathrm{I} k \; (\frac{r}{R}\theta_t)} \, \mathrm{e}^{2\pi\mathrm{i} r s / R} \qquad(t \in I_T, s \in I_R). \]](form_260.png)
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include "util.h"
#include "nfft3.h"
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 | Inverse_Radon_trafo (int(*gridfcn)(), int T, int R, double *Rf, int NN, double *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 | |
Computes the inverse of the discrete Radon transform
given at the points 
of the polar or linogram grid and where 
are the weights of the Dirichlet- or Fejer-kernel by 1D-FFTs and the 2D-iNFFT.
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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 < index for nodes and freqencies < plan for the nfft-2D < plan for the inverse nfft < variable for the fftw-1Ds < plan for the fftw-1Ds < index for directions and offsets < knots and associated weights < index for iterations init two dimensional NFFT plan init two dimensional infft plan init nodes and weights of grid precompute psi, the entries of the matrix B compute 1D-ffts and init given samples and weights initialise some guess f_hat_0 solve the system copy result finalise the plans and free the variables |
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simple test program for the inverse discrete Radon transform < grid generating function < number of directions/offsets < image size < number of iterations load data inverse Radon transform write result free the variables |
1.4.4