Prolate spheroidal wavelet sampling in computerized tomography

Abstract

In computerized tomography, an image must be recovered from data given by the Radon transform of the image. This data is usually in the form of sampled values of the transform. In this work, a method of recovering the image is based on the sampling properties of the prolate spheroidal wavelets which are superior to other wavelets. It avoids integration and allows the precomputation of certain coefficients. The approximation based on this method is shown to converge to the true image under mild hypotheses. The algorithm is then tested on the standard Shepp-Logan image and shown to be surprisingly good. © 2006 Sampling Publishing.