Nonequispaced fast Fourier transform
Radon transform, CT
Nonequispaced fast Fourier transform 

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.

Phantom
Sinogram
Reconstructed phantom

Figure: Left to right: phantom, sinogram, and 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 authors 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 of slices of thorax data

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

References

  • Potts, D. and Steidl, G.
    A new linogram algorithm for computerized tomography.
    IMA J. Numer. Anal. 21, 769–782, 2001. pdf ps
  • Potts, 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, 2000. pdf ps