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UNMATCHED PROJECTOR/BACKPROJECTOR PAIRS: PERTURBATION AND CONVERGENCE ANALYSIS
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
Tech Univ Denmark, Denmark.
2018 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 40, no 1, p. A573-A591Article in journal (Refereed) Published
Abstract [en]

In tomographic reconstruction problems it is not uncommon that there are errors in the implementation of the forward projector and/or the backprojector, and hence we encounter a so-called unmatched projektor/backprojector pair. Consequently, the matrices that represent the two projectors are not each others transpose. Surprisingly, the influence of such errors in algebraic iterative reconstruction methods has received little attention in the literature. The goal of this paper is to perform a rigorous first-order perturbation analysis of the minimization problems underlying the algebraic methods in order to understand the role played by the nonmatch of the matrices. We also study the convergence properties of linear stationary iterations based on unmatched matrix pairs, leading to insight into the behavior of some important row-and column-oriented algebraic iterative methods. We conclude with numerical examples that illustrate the perturbation and convergence results.

Place, publisher, year, edition, pages
SIAM PUBLICATIONS , 2018. Vol. 40, no 1, p. A573-A591
Keywords [en]
perturbation theory; convergence analysis; algebraic iterative reconstruction; semiconvergence; computed tomography
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-147178DOI: 10.1137/17M1133828ISI: 000426743500024OAI: oai:DiVA.org:liu-147178DiVA, id: diva2:1199458
Note

Funding Agencies|European Research Council [291405]

Available from: 2018-04-20 Created: 2018-04-20 Last updated: 2018-04-20

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  • nn-NB
  • sv-SE
  • Other locale
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Output format
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