Generalized Row-Action Methods for Tomographic Imaging

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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.
Original languageEnglish
JournalNumerical Algorithms
Volume67
Issue number1
Pages (from-to)121
Number of pages144
ISSN1017-1398
DOIs
Publication statusPublished - 2014

Keywords

  • Incremental methods
  • Proximal methods
  • Inverse Problems
  • Regularization
  • Tomographic Imaging

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