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...

Full description

Saved in:
Bibliographic Details
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
Online AccessGet full text
ISSN1068-9613
1097-4067

Cover

More Information
Summary: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
ISSN:1068-9613
1097-4067