On regularization methods of EM-Kaczmarz type

TL;DR

This paper introduces stabilized regularization extensions of the EM-Kaczmarz and OS-EM algorithms for solving ill-posed equations with noisy data, demonstrating improved convergence speed and stability.

Contribution

It proposes new regularization methods of Kaczmarz type linked to EM, enhancing stability and speed over standard algorithms for ill-posed problems.

Findings

Extended OS-EM methods are significantly faster than standard EM.

The methods exhibit monotonicity properties.

Numerical experiments confirm improved performance.

Abstract

We consider regularization methods of Kaczmarz type in connection with the expectation-maximization (EM) algorithm for solving ill-posed equations. For noisy data, our methods are stabilized extensions of the well established ordered-subsets expectation-maximization iteration (OS-EM). We show monotonicity properties of the methods and present a numerical experiment which indicates that the extended OS-EM methods we propose are much faster than the standard EM algorithm.