Semi-convergence and relaxation parameters for a class of SIRT algorithms

Tommy Elfving; Touraj Nikazad; Per Christian Hansen

Semi-convergence and relaxation parameters for a class of SIRT algorithms

Tommy Elfving, Touraj Nikazad, Per Christian Hansen

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

This paper is concerned with the Simultaneous Iterative Reconstruction Technique (SIRT) class of iterative methods for solving inverse problems. Based on a careful analysis of the semi-convergence behavior of these methods, we propose two new techniques to specify the relaxation parameters adaptively during the iterations, so as to control the propagated noise component of the error. The advantage of using this strategy for the choice of relaxation parameters on noisy and ill-conditioned problems is demonstrated with an example from tomography (image reconstruction from projections).

Original language	English
Journal	Electronic Transactions on Numerical Analysis
Volume	37
Pages (from-to)	321-336
ISSN	1068-9613
Publication status	Published - 2010

Keywords

Semi-convergence
Relaxation parameters
SIRT methods
Tomographic imaging
Cimmino and DROP iteration

Access to Document

http://etna.mcs.kent.edu/vol.37.2010/pp321-336.dir/pp321-336.pdf

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title = "Semi-convergence and relaxation parameters for a class of SIRT algorithms",

abstract = "This paper is concerned with the Simultaneous Iterative Reconstruction Technique (SIRT) class of iterative methods for solving inverse problems. Based on a careful analysis of the semi-convergence behavior of these methods, we propose two new techniques to specify the relaxation parameters adaptively during the iterations, so as to control the propagated noise component of the error. The advantage of using this strategy for the choice of relaxation parameters on noisy and ill-conditioned problems is demonstrated with an example from tomography (image reconstruction from projections).",

keywords = "Semi-convergence, Relaxation parameters, SIRT methods, Tomographic imaging, Cimmino and DROP iteration",

author = "Tommy Elfving and Touraj Nikazad and Hansen, {Per Christian}",

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journal = "Electronic Transactions on Numerical Analysis",

issn = "1068-9613",

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T1 - Semi-convergence and relaxation parameters for a class of SIRT algorithms

AU - Elfving, Tommy

AU - Nikazad, Touraj

AU - Hansen, Per Christian

PY - 2010

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N2 - This paper is concerned with the Simultaneous Iterative Reconstruction Technique (SIRT) class of iterative methods for solving inverse problems. Based on a careful analysis of the semi-convergence behavior of these methods, we propose two new techniques to specify the relaxation parameters adaptively during the iterations, so as to control the propagated noise component of the error. The advantage of using this strategy for the choice of relaxation parameters on noisy and ill-conditioned problems is demonstrated with an example from tomography (image reconstruction from projections).

AB - This paper is concerned with the Simultaneous Iterative Reconstruction Technique (SIRT) class of iterative methods for solving inverse problems. Based on a careful analysis of the semi-convergence behavior of these methods, we propose two new techniques to specify the relaxation parameters adaptively during the iterations, so as to control the propagated noise component of the error. The advantage of using this strategy for the choice of relaxation parameters on noisy and ill-conditioned problems is demonstrated with an example from tomography (image reconstruction from projections).

KW - Semi-convergence

KW - Relaxation parameters

KW - SIRT methods

KW - Tomographic imaging

KW - Cimmino and DROP iteration

M3 - Journal article

VL - 37

SP - 321

EP - 336

JO - Electronic Transactions on Numerical Analysis

JF - Electronic Transactions on Numerical Analysis

SN - 1068-9613

ER -