Convergence analysis for column-action methods in image reconstruction |
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Authors: | Tommy Elfving Per Christian Hansen Touraj Nikazad |
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Affiliation: | 1.Department of Mathematics,Link?ping University,Link?ping,Sweden;2.Department of Applied Mathematics and Computer Science,Technical University of Denmark,Kgs. Lyngby,Denmark;3.School of Mathematics,Iran University of Science and Technology,Narmak,Iran |
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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. |
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