Convergence analysis for column-action methods in image reconstruction

Tommy Elfving, Per Christian Hansen, Touraj Nikazad

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Abstract

Column-oriented versions of algebraic iterative methods are interesting alternatives to their row-version counterparts: they converge to a least squares solution, and they provide a basis for saving computational work by skipping small updates. In this paper we consider the case of noise-free data. We present a convergence analysis of the column algorithms, we discuss two techniques (loping and flagging) for reducing the work, and we establish some convergence results for methods that utilize these techniques. The performance of the algorithms is illustrated with numerical examples from computed tomography.
Original languageEnglish
JournalNumerical Algorithms
Volume74
Issue number3
Pages (from-to)905–924
ISSN1017-1398
DOIs
Publication statusPublished - 2016

Keywords

  • Algebraic iterative reconstruction
  • Block-iteration
  • ART
  • Kaczmarz
  • Cimmino
  • Convergence

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