Inversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery principles
Autor(a) principal: | |
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Data de Publicação: | 2011 |
Outros Autores: | , , |
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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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 |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799136972145426432 |