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Indirect image registration with large diffeomorphic deformations
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-1118-6483
2018 (English)In: SIAM Journal on Imaging Sciences, ISSN 1936-4954, E-ISSN 1936-4954, Vol. 11, no 1, p. 575-617Article in journal (Refereed) Published
Abstract [en]

This paper adapts the large deformation diffeomorphic metric mapping framework for image registration to the indirect setting, where a template is registered against a target that is given through indirect noisy observations. The registration uses diffeomorphisms that transform the template through a (group) action. These diffeomorphisms are generated by solving a flow equation that is defined by a velocity field with certain regularity. The theoretical analysis includes a proof that indirect image registration has solutions (existence) that are stable and that converge as the data error tends to zero, so it becomes a well-defined regularization method. The paper concludes with examples of indirect image registration in 2D tomography with very sparse and/or highly noisy data. 

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics Publications , 2018. Vol. 11, no 1, p. 575-617
Keywords [en]
Diffeomorphisms, Image reconstruction, Indirect image registration, Large deformations, Shape regularization, Shape theory, Tomography, Deformation, Image registration, Velocity, Diffeomorphic deformation, Large deformation diffeomorphic metric mappings, Noisy observations, Regularization methods, Velocity field
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-227421DOI: 10.1137/17M1134627ISI: 000428946200019Scopus ID: 2-s2.0-85045630390OAI: oai:DiVA.org:kth-227421DiVA, id: diva2:1210590
Note

Export Date: 9 May 2018; Article; Funding details: KTH, Kungliga Tekniska Högskolan; Funding details: 100190, CAS, Chinese Academy of Sciences; Funding details: AM13-0049, SSF, Stiftelsen för Strategisk Forskning; Funding details: 11301520, NSFC, National Natural Science Foundation of China; Funding details: NSFC, National Natural Science Foundation of China; Funding text: ∗Received by the editors June 14, 2017; accepted for publication (in revised form) December 18, 2017; published electronically March 1, 2018. http://www.siam.org/journals/siims/11-1/M113462.html Funding: This work was supported by the Swedish Foundation for Strategic Research grant AM13-0049. The first author was also supported in part by the National Natural Science Foundation of China (NSFC) under grant 11301520. †LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China (chench@lsec.cc.ac.cn). ‡Department of Mathematics, KTH–Royal Institute of Technology, 100 44 Stockholm, Sweden (ozan@kth.se). QC 20180529

Available from: 2018-05-29 Created: 2018-05-29 Last updated: 2018-05-29Bibliographically approved

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Öktem, Ozan

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