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Semi-convergence properties of Kaczmarzs method
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
Technical University of Denmark, Denmark .
Iran University of Science and Technology, Iran .
2014 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 30, no 5, 055007- p.Article in journal (Refereed) Published
Abstract [en]

Kaczmarzs method-sometimes referred to as the algebraic reconstruction technique-is an iterative method that is widely used in tomographic imaging due to its favorable semi-convergence properties. Specifically, when applied to a problem with noisy data, during the early iterations it converges very quickly toward a good approximation of the exact solution, and thus produces a regularized solution. While this property is generally accepted and utilized, there is surprisingly little theoretical justification for it. The purpose of this paper is to present insight into the semi-convergence of Kaczmarzs method as well as its projected counterpart (and their block versions). To do this we study how the data errors propagate into the iteration vectors and we derive upper bounds for this noise propagation. Our bounds are compared with numerical results obtained from tomographic imaging.

Place, publisher, year, edition, pages
IOP Publishing: Hybrid Open Access , 2014. Vol. 30, no 5, 055007- p.
Keyword [en]
Kaczmarzs method; ART; sequential iterative reconstruction technique; semi-convergence; non-negativity constraints; tomographic imaging
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-107846DOI: 10.1088/0266-5611/30/5/055007ISI: 000336265400007OAI: diva2:727715
Available from: 2014-06-23 Created: 2014-06-23 Last updated: 2014-06-23

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