Superiorization of Incremental Optimization Algorithms for Statistical Tomographic Image Reconstruction

TL;DR

This paper introduces superiorization techniques for incremental algorithms in tomographic image reconstruction, improving their convergence towards Pareto optimal solutions through new methods and theoretical analysis.

Contribution

It presents novel superiorization schemes for incremental algorithms, including a new scaled gradient iteration, with theoretical validation and experimental evaluation.

Findings

Superiorized algorithms are closer to Pareto optimal solutions.

The new scaled gradient iteration enhances convergence.

Experimental results demonstrate improved reconstruction quality.

Abstract

We propose the superiorization of incremental algorithms for tomographic image reconstruction. The resulting methods follow a better path in its way to finding the optimal solution for the maximum likelihood problem in the sense that they are closer to the Pareto optimal curve than the non-superiorized techniques. A new scaled gradient iteration is proposed and three superiorization schemes are evaluated. Theoretical analysis of the methods as well as computational experiments with both synthetic and real data are provided.