On the use of wavelets in inverting the Radon transform

Abstract

Some new results on constrained image reconstruction are presented. Given constraints on pixel values and the statistics of additive noise in the projections, it is shown how to compute the minimum mean-square estimate of the reconstructed image. The authors also present some results on the use of the wavelet transform to perform spatially varying filtering of the image and show how noise can be suppressed in flat areas of the image. They then combine the previous results into a new constrained image reconstruction procedure, in which image constraints are applied in the wavelet domain. The new procedure improves the reconstructed image not only in locations where wavelet constraints are applied, but also in other regions.<>