A Modified Kaczmarz Algorithm for Computerized Tomographic Image Reconstruction

Abstract

A modified version of Kaczmarz algorithm for improving image reconstruction from projections in computerized tomography is proposed. Instead of taking projection onto hyperplanes sequentially in the given order in each iteration by classical Kaczmarz algorithm, the proposed algorithm does projection in an adaptive order which is evaluated from pseudo measurement error of each hyperplane. Since this algorithm proceeds with a basic aspect of traditional Kaczmarz algorithm, it can suit a variety of Kaczmarz extended algorithm. Numerical experiments described in the last part of the paper indicate that the Modified Kaczmarz algorithm gives much better results than the classical one. Keywords-image reconstruction;Kaczmarz algorithm; iterative techniques; sparse systems; tomography