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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.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark

    Martin S. Andersen & Per Christian Hansen

Authors
  1. Martin S. Andersen
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  2. Per Christian Hansen
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Correspondence to Per Christian Hansen.

Additional information

This work is part of the project High-Definition Tomography and it is supported by Grant No. ERC-2011-ADG 20110209 from the European Research Council.

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Andersen, M.S., Hansen, P.C. Generalized row-action methods for tomographic imaging. Numer Algor 67, 121–144 (2014). https://doi.org/10.1007/s11075-013-9778-8

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