Limited angle tomography via multiresolution analysis and oversampling

Abstract

A method is presented for reconstructing a function from its line integrals. This problem arises in imaging whenever the physical constraints of the system prohibit the gathering of the line integrals over the angles - pi /2< theta <0. The first portion of the algorithm decomposes the limited angle operator L into a tensor product structure that allows an efficient calculation of its singular value decomposition. The second portion of the algorithm uses multiresolution analysis in order to mollify the problem, which is known to be extremely ill conditioned. It is thought that these methods may lead to a more stable algorithm for limited angle reconstruction.<>