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Multiresolution Parameter Choice Method for Total Variation Regularized Tomography
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
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2016 (English)In: SIAM Journal of Imaging Sciences, ISSN 1936-4954, E-ISSN 1936-4954, Vol. 9, no 3, 938-974 p.Article in journal (Refereed) Published
Abstract [en]

A computational method is introduced for choosing the regularization parameter for total variation (TV) regularization. A partial understanding of the properties of the method is provided by rigorously proving that the TV norms of the reconstructions converge with any choice of regularization parameter. The computational approach is based on computing reconstructions at a few different resolutions and various values of regularization parameter. The chosen parameter is the smallest one resulting in approximately discretization-invariant TV norms of the reconstructions. The method is tested with simulated and experimental X-ray tomography data and compared to the S-curve method. The results are comparable to those of the S-curve method. However, the S-curve method needs quantitative a priori information about the expected sparsity (TV norm) of the unknown, while the proposed method does not require such input parameters.

Place, publisher, year, edition, pages
SIAM PUBLICATIONS , 2016. Vol. 9, no 3, 938-974 p.
Keyword [en]
total variation regularization, parameter choice, tomography, inverse problem, regularization
National Category
Computer Science
Identifiers
URN: urn:nbn:se:kth:diva-196490DOI: 10.1137/15M1034076ISI: 000385277200003ScopusID: 2-s2.0-84989321781OAI: oai:DiVA.org:kth-196490DiVA: diva2:1049294
Note

QC 20161124

Available from: 2016-11-24 Created: 2016-11-14 Last updated: 2016-11-24Bibliographically approved

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Niinimäki, Kati
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Mathematics (Div.)
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