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Joint Gaussian dictionary learning and tomographic reconstruction
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-7472-5325
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-1118-6483
Etud & Prod Schlumberger, 1 Rue Henri Becquerel, F-92140 Clamart, France..
2022 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 38, no 10, article id 105010Article in journal (Refereed) Published
Abstract [en]

This paper studies ill-posed tomographic imaging problems where the image is sparsely represented by a non-negative linear combination of Gaussians. Our main contribution is to develop a scheme for directly recovering the Gaussian mixture representation of an image from tomographic data, which here is modeled as noisy samples of the parallel-beam ray transform. An important aspect of this non-convex reconstruction problem is the choice of initial guess. We propose an initialization procedure that is based on a filtered back projection type of operator tailored for the Gaussian dictionary. This operator can be evaluated efficiently using an approximation of the Riesz-potential of an anisotropic Gaussian which is based on an exact closed form expression for the Riesz-potential of an isotropic Gaussian. The proposed method is evaluated on simulated data.

Place, publisher, year, edition, pages
IOP Publishing , 2022. Vol. 38, no 10, article id 105010
Keywords [en]
dictionary learning, inverse problem, tomography, task adapted reconstruction, image reconstruction, sparse coding, regularization
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering Computational Mathematics Other Physics Topics
Identifiers
URN: urn:nbn:se:kth:diva-318234DOI: 10.1088/1361-6420/ac8beeISI: 000851299600001Scopus ID: 2-s2.0-85138442706OAI: oai:DiVA.org:kth-318234DiVA, id: diva2:1697067
Note

QC 20220920

Available from: 2022-09-20 Created: 2022-09-20 Last updated: 2023-05-22Bibliographically approved

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Zickert, GustavÖktem, Ozan

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CiteExportLink to record
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  • apa
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  • de-DE
  • en-GB
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Output format
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  • asciidoc
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