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Convergence analysis for column-action methods in image reconstruction

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An Erratum to this article was published on 18 November 2016

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.

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Authors and Affiliations

  1. Department of Mathematics, Linköping University, 581 83, Linköping, Sweden

    Tommy Elfving

  2. Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800, Kgs. Lyngby, Denmark

    Per Christian Hansen

  3. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran

    Touraj Nikazad

Authors
  1. Tommy Elfving
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  2. Per Christian Hansen
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  3. Touraj Nikazad
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Corresponding author

Correspondence to Per Christian Hansen.

Additional information

This work is a part of the project HD-Tomo funded by Advanced Grant No. 291405 from the European Research Council.

An erratum to this article is available at http://dx.doi.org/10.1007/s11075-016-0232-6.

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Elfving, T., Hansen, P.C. & Nikazad, T. Convergence analysis for column-action methods in image reconstruction. Numer Algor 74, 905–924 (2017). https://doi.org/10.1007/s11075-016-0176-x

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