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Generalized Sinkhorn Iterations for Regularizing Inverse Problems Using Optimal Mass Transport
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0001-5158-9255
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0002-9778-1426
2017 (English)In: SIAM Journal on Imaging Sciences, ISSN 1936-4954, E-ISSN 1936-4954, Vol. 10, no 4, p. 1935-1962Article in journal (Refereed) Published
Abstract [en]

The optimal mass transport problem gives a geometric framework for optimal allocation and has recently attracted significant interest in application areas such as signal processing, image processing, and computer vision. Even though it can be formulated as a linear programming problem, it is in many cases intractable for large problems due to the vast number of variables. A recent development addressing this builds on an approximation with an entropic barrier term and solves the resulting optimization problem using Sinkhorn iterations. In this work we extend this methodology to a class of inverse problems. In particular we show that Sinkhorn-type iterations can be used to compute the proximal operator of the transport problem for large problems. A splitting framework is then used to solve inverse problems where the optimal mass transport cost is used for incorporating a priori information. We illustrate this method on problems in computerized tomography. In particular we consider a limited-angle computerized tomography problem, where a priori information is used to compensate for missing measurements.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2017. Vol. 10, no 4, p. 1935-1962
Keywords [en]
inverse problems, optimal mass transport, Sinkhorn iterations, proximal methods, variable split- ting, medical imaging
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-219364DOI: 10.1137/17M111208XISI: 000418654000009Scopus ID: 2-s2.0-85039745826OAI: oai:DiVA.org:kth-219364DiVA, id: diva2:1162499
Funder
Swedish Research Council, 2014-5870Swedish Foundation for Strategic Research , AM13-0049
Note

QC 20171212

Available from: 2017-12-04 Created: 2017-12-04 Last updated: 2018-01-16Bibliographically approved

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