Ridgelet analysis and application to image reconstruction

Abstract

Candes introduced the notion of ridgelets and showed how they can be applied to solve important problems such as approximating and estimating multivariate functions by linear combinations of ridge functions. We do tomographic reconstruction experiment. Unlike Fourier or wavelet methods, two dimensional ridgelets provide optimally sparse representations of smooth functions with discontinuities along edges, i.e, straight lines. Our experiments turn out to be quite successful in many respects, especially noise reduction.