Generalized Row-Action Methods for Tomographic Imaging

TL;DR

This paper introduces relaxed incremental proximal gradient methods that unify and extend row-action algorithms for tomographic imaging, enabling incorporation of prior information and demonstrating fast initial convergence in practical reconstructions.

Contribution

It proposes a generalized class of incremental algorithms for tomography, allowing flexible regularization and improving upon existing row-action methods.

Findings

Algorithms show fast initial convergence in numerical tests.

New methods effectively incorporate prior information.

Demonstrated improved reconstruction quality.

Abstract

Row-action methods play an important role in tomographic image reconstruction. Many such methods can be viewed as incremental gradient methods for minimizing a sum of a large number of convex functions, and despite their relatively poor global rate of convergence, these methods often exhibit fast initial convergence which is desirable in applications where a low-accuracy solution is acceptable. In this paper, we propose relaxed variants of a class of incremental proximal gradient methods, and these variants generalize many existing row-action methods for tomographic imaging. Moreover, they allow us to derive new incremental algorithms for tomographic imaging that incorporate different types of prior information via regularization. We demonstrate the efficacy of the approach with some numerical examples.