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A new variational model for joint image reconstruction and motion estimation in spatiotemporal imaging
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-1118-6483
2019 (English)In: SIAM Journal on Imaging Sciences, E-ISSN 1936-4954, Vol. 12, no 4, p. 1686-1719Article in journal (Refereed) Published
Abstract [en]

We propose a new variational model for joint image reconstruction and motion estimation in spatiotemporal imaging, which is investigated along a general framework that we present with shape theory. This model consists of two components, one for conducting modified static image reconstruction, and the other performs sequentially indirect image registration. For the latter, we generalize the large deformation diffeomorphic metric mapping framework into the sequentially indirect registration setting. The proposed model is compared theoretically against alternative approaches (optical flow based model and diffeomorphic motion models), and we demonstrate that the proposed model has desirable properties in terms of the optimal solution. The theoretical derivations and efficient algorithms are also presented for a time-discretized scenario of the proposed model, which show that the optimal solution of the time-discretized version is consistent with that of the time-continuous one, and most of the computational components is the easy-implemented linearized deformation. The complexity of the algorithm is analyzed as well. This work is concluded by some numerical examples in 2D space + time tomography with very sparse and/or highly noisy data.

Place, publisher, year, edition, pages
Society for Industrial & Applied Mathematics (SIAM) , 2019. Vol. 12, no 4, p. 1686-1719
Keywords [en]
Image reconstruction, Joint variational model, Large diffeomorphic deformations, Motion estimation, Shape theory, Spatiotemporal imaging, Computational complexity, Computational efficiency, Deformation, Optimal systems, Computational components, Diffeomorphic deformation, Joint image reconstruction, Large deformation diffeomorphic metric mappings, Optimal solutions, Theoretical derivations, Variational modeling
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-268577DOI: 10.1137/18M1234047ISI: 000545944800005Scopus ID: 2-s2.0-85077059129OAI: oai:DiVA.org:kth-268577DiVA, id: diva2:1428699
Funder
Swedish Foundation for Strategic Research, AM13-0049
Note

QC 20200506

Available from: 2020-05-06 Created: 2020-05-06 Last updated: 2024-04-25Bibliographically approved

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Öktem, Ozan

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CiteExportLink to record
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  • apa
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Output format
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  • asciidoc
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