Kaczmarz Anomaly in Tomography Problems

Abstract

The Kaczmarz method is an important tool for solving large sparse linear systems that arise in computerized tomography. The Kaczmarz anomaly phenomenon has been observed recently when solving certain types of random systems. This raises the question of whether a similar anomaly occurs in tomography problems. The aim of the paper is to answer this question, to examine the extent of the phenomenon and to explain its reasons. Another tested issue is the ability of random row shuffles to sharpen the anomaly and to accelerate the rate of convergence. The results add important insight into the nature of the Kaczmarz method.