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Inversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery principles

2011-11Journal article Open access
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dc.contributor.authorCerejeiras, Paula
dc.contributor.authorFerreira, Milton
dc.contributor.authorKaehler, Uwe
dc.contributor.authorTeschke, Gerd
dc.date.accessioned2019-02-07T15:12:15Z
dc.date.available2019-02-07T15:12:15Z
dc.date.issued2011-11
dc.descriptionAcknowledgements: The research of P. Cerejeiras, M. Ferreira, and U. Kähler was (partially) supported by Unidade de Investigação Matemática e Aplicações of Universidade de Aveiro, through Programa Operacional Ciência, Tecnologia, Inovação (POCTI) of the Fundação para a Ciência e a Tecnologia (FCT), co nanced by the European Community fund FEDER. G. Teschke gratefully acknowledges support by DAAD Grant D/07/13641
dc.description.abstractThe inversion of the one-dimensional Radon transform on the rotation group SO(3) is an ill-posed inverse problem that can be applied to X-ray tomography with polycrystalline materials. This paper is concerned with the development of a method to stably approximate the inverse of the noisy Radon transform on SO(3). The proposed approach is composed by basic building blocks of the coorbit theory on homogeneous spaces, Gabor frame constructions and variational principles for sparse recovery. The performance of the finally obtained iterative approximation is studied through several experiments.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationCerejeiras P., Ferreira M., Kähler U., and Teschke G., Inversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery algorithms, Appl. Comput. Harmon. Anal., 31 (3) (2011), 325-345pt_PT
dc.identifier.doi10.1016/j.acha.2011.01.005pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.8/3815
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherElsevierpt_PT
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/pii/S1063520311000194pt_PT
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/pt_PT
dc.subjectRadon transform onpt_PT
dc.subjectSO(3)pt_PT
dc.subjectX-ray tomographypt_PT
dc.subjectGabor framespt_PT
dc.subjectCoorbit theorypt_PT
dc.subjectSparse recoverypt_PT
dc.subjectCrystallographypt_PT
dc.titleInversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery principlespt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage345pt_PT
oaire.citation.issue3pt_PT
oaire.citation.startPage325pt_PT
oaire.citation.titleApplied and Computational Harmonic Analysispt_PT
oaire.citation.volume31pt_PT
person.familyNameCerejeiras
person.familyNameFerreira
person.familyNameKaehler
person.givenNamePaula
person.givenNameMilton
person.givenNameUwe
person.identifier.ciencia-id1C1F-9AC1-4CC1
person.identifier.ciencia-idCA19-2009-F26D
person.identifier.ciencia-id9719-A120-F245
person.identifier.orcid0000-0001-7667-4595
person.identifier.orcid0000-0003-1816-8293
person.identifier.orcid0000-0002-9066-1819
person.identifier.ridA-2004-2015
person.identifier.scopus-author-id8845778900
person.identifier.scopus-author-id12144179800
person.identifier.scopus-author-id36191910600
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublication3a16d178-cb0f-4210-9a39-d452715f6355
relation.isAuthorOfPublicationb1460cdc-4ced-46c6-a637-68b425d104dc
relation.isAuthorOfPublicationff6e7bb4-05b0-4efb-a5a4-672705aa0748
relation.isAuthorOfPublication.latestForDiscovery3a16d178-cb0f-4210-9a39-d452715f6355

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