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

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 adaptivel...

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Published inElectronic transactions on numerical analysis Vol. 37; p. 321
Main Authors Elfving, Tommy, Nikazad, Touraj, Hansen, Per Christian
Format Journal Article
LanguageEnglish
Published Institute of Computational Mathematics 01.01.2010
Subjects
Algorithms
Cimmino and DROP iteration
relaxation parameters
semi-convergence
SIRT methods
TECHNOLOGY
TEKNIKVETENSKAP
tomographic imaging
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ISSN1068-9613
1097-4067

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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). Key words. SIRT methods, Cimmino and DROP iteration, semi-convergence, relaxation parameters, tomographic imaging AMS subject classifications. 65F10, 65R32
AbstractList 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). Key words. SIRT methods, Cimmino and DROP iteration, semi-convergence, relaxation parameters, tomographic imaging AMS subject classifications. 65F10, 65R32
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
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).
Audience Academic
Author Hansen, Per Christian
Nikazad, Touraj
Elfving, Tommy
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Snippet This paper is concerned with the Simultaneous Iterative Reconstruction Technique (SIRT) class of iterative methods for solving inverse problems. Based on a...
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StartPage 321
SubjectTerms Algorithms
Cimmino and DROP iteration
relaxation parameters
semi-convergence
SIRT methods
TECHNOLOGY
TEKNIKVETENSKAP
tomographic imaging
Title Semi-convergence and relaxation parameters for a class of SIRT algorithms
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Volume 37
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