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

Detalhes bibliográficos
Autor(a) principal: Cerejeiras, Paula
Data de Publicação: 2011
Outros Autores: Ferreira, Milton, Kaehler, Uwe, Teschke, Gerd
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.8/3815
Resumo: Acknowledgements: 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
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spelling Inversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery principlesRadon transform onSO(3)X-ray tomographyGabor framesCoorbit theorySparse recoveryCrystallographyAcknowledgements: 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/07/13641The 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.ElsevierIC-OnlineCerejeiras, PaulaFerreira, MiltonKaehler, UweTeschke, Gerd2019-02-07T15:12:15Z2011-112011-11-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.8/3815engCerejeiras 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), 325-34510.1016/j.acha.2011.01.005info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-17T15:47:58Zoai:iconline.ipleiria.pt:10400.8/3815Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:47:50.444194Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Inversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery principles
title Inversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery principles
spellingShingle Inversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery principles
Cerejeiras, Paula
Radon transform on
SO(3)
X-ray tomography
Gabor frames
Coorbit theory
Sparse recovery
Crystallography
title_short Inversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery principles
title_full Inversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery principles
title_fullStr Inversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery principles
title_full_unstemmed Inversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery principles
title_sort Inversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery principles
author Cerejeiras, Paula
author_facet Cerejeiras, Paula
Ferreira, Milton
Kaehler, Uwe
Teschke, Gerd
author_role author
author2 Ferreira, Milton
Kaehler, Uwe
Teschke, Gerd
author2_role author
author
author
dc.contributor.none.fl_str_mv IC-Online
dc.contributor.author.fl_str_mv Cerejeiras, Paula
Ferreira, Milton
Kaehler, Uwe
Teschke, Gerd
dc.subject.por.fl_str_mv Radon transform on
SO(3)
X-ray tomography
Gabor frames
Coorbit theory
Sparse recovery
Crystallography
topic Radon transform on
SO(3)
X-ray tomography
Gabor frames
Coorbit theory
Sparse recovery
Crystallography
description Acknowledgements: 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
publishDate 2011
dc.date.none.fl_str_mv 2011-11
2011-11-01T00:00:00Z
2019-02-07T15:12:15Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.8/3815
url http://hdl.handle.net/10400.8/3815
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Cerejeiras 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), 325-345
10.1016/j.acha.2011.01.005
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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