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Nonequispaced fast Fourier transform
Radon transform, CT

Radon transform and computer tomography

The folder ./applications/radon includes simple C programs (radon.c, inverse_radon.c) for the computation of a fast discrete NFFT-based Radon transform and its inverse. Use the Matlab script file radon.m for a simple demonstration.

Left to right: phantom, sinogram, and reconstructed phantom
phantom sinogram reconstructed phantom

The following animation shows, some slices of thorax data. The reconstruction was done with Algorithm 3.3 from the paper ``New Fourier reconstruction algorithms for computerized tomography'' after a rebinning. The autors wish to thank M. Ebert from DKFZ-Heidelberg for giving us the data from Somatom Plus 4 and N. Papenberg (MUL Lübeck) for producing the animation.
Animation slices of thorax data

The algorithms are implemented by Markus Fenn in ./applications/radon. Related paper are

oPotts, D. and Steidl, G.
A new linogram algorithm for computerized tomography.
IMA J. Numer. Anal. 21, 769-782. (full paper ps, pdf),   2001

oPotts, D. and Steidl, G.
New Fourier reconstruction algorithms for computerized tomography.
in: Proceedings of SPIE: Wavelet Applications in Signal and Image Processing VIII,A. Aldroubi,A.F. Laine,M.A. Unser (Eds.), Vol.:4119, pages 13-23. (full paper ps, pdf),   2000