Nonequispaced fast Fourier transform
Ridgelet transform
Nonequispaced fast Fourier transform 

Ridgelet transform

The discrete ridgelet transform is designed by first using a discrete Radon transform based on the nonequispaced fast Fourier transform and then applying a dual-tree complex wavelet transform.

The Matlab script file ridgelet.m (see the folder ./examples/radon) contains an example of denoising by hard thresholding the discrete ridgelet coefficients of a noisy image. The discrete ridgelet transform is based on the fast discrete NFFT-based Radon transform and the translation-invariant discrete wavelet transform of the free Matlab toolbox WaveLab850.

Original image
Noisy image
Reconstructed image

Figure: Left to right: original image, noisy image (SNR=1), and reconstructed image (SNR=12.55).

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

References

  • Fenn, M. and Ma, J.
    Combined complex ridgelet shrinkage and total variation minimization.
    SIAM J. Sci. Comput. 28, 984–1000, 2006.