Difference factorizations and monotonicity in inverse medium scattering for contrasts with fixed sign on the boundary
Autor(a) principal: | |
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Data de Publicação: | 2016 |
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/10773/16247 |
Resumo: | We generalize the factorization method for inverse medium scattering using a particular factorization of the difference of two far field operators. While the factorization method has been used so far mainly to identify the shape of a scatterer's support, we show that factorizations based on Dirichlet-to-Neumann operators can be used to compute bounds for numerical values of the medium on the boundary of its support. To this end, we generalize ideas from inside-outside duality to obtain a monotonicity principle that allows for alternative uniqueness proofs for particular inverse scattering problems (e.g., when obstacles are present inside the medium). This monotonicity principle indeed is our most important technical tool: It further directly shows that the boundary values of the medium's contrast function are uniquely determined by the corresponding far field operator. Our particular factorization of far field operators additionally implies that the factorization method rigorously characterizes the support of an inhomogeneous medium if the contrast function takes merely positive or negative values on the boundary of its support independently of the contrast's values inside its support. Finally, the monotonicity principle yields a simple algorithm to compute upper and lower bounds for these boundary values, assuming the support of the contrast is known. Numerical experiments show feasibility of a resulting numerical algorithm. |
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Difference factorizations and monotonicity in inverse medium scattering for contrasts with fixed sign on the boundaryInverse scatteringFactorizationMonotonicityCharacterization of boundary valuesWe generalize the factorization method for inverse medium scattering using a particular factorization of the difference of two far field operators. While the factorization method has been used so far mainly to identify the shape of a scatterer's support, we show that factorizations based on Dirichlet-to-Neumann operators can be used to compute bounds for numerical values of the medium on the boundary of its support. To this end, we generalize ideas from inside-outside duality to obtain a monotonicity principle that allows for alternative uniqueness proofs for particular inverse scattering problems (e.g., when obstacles are present inside the medium). This monotonicity principle indeed is our most important technical tool: It further directly shows that the boundary values of the medium's contrast function are uniquely determined by the corresponding far field operator. Our particular factorization of far field operators additionally implies that the factorization method rigorously characterizes the support of an inhomogeneous medium if the contrast function takes merely positive or negative values on the boundary of its support independently of the contrast's values inside its support. Finally, the monotonicity principle yields a simple algorithm to compute upper and lower bounds for these boundary values, assuming the support of the contrast is known. Numerical experiments show feasibility of a resulting numerical algorithm.Society for Industrial and Applied Mathematics2016-11-04T15:31:37Z2016-11-01T00:00:00Z2016-11info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/16247eng0036-141010.1137/16M1060819Lechleiter, ArminLakshtanov, Evgenyinfo: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:RCAAP2024-02-22T11:30:13Zoai:ria.ua.pt:10773/16247Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:51:24.320772Repositório 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 |
Difference factorizations and monotonicity in inverse medium scattering for contrasts with fixed sign on the boundary |
title |
Difference factorizations and monotonicity in inverse medium scattering for contrasts with fixed sign on the boundary |
spellingShingle |
Difference factorizations and monotonicity in inverse medium scattering for contrasts with fixed sign on the boundary Lechleiter, Armin Inverse scattering Factorization Monotonicity Characterization of boundary values |
title_short |
Difference factorizations and monotonicity in inverse medium scattering for contrasts with fixed sign on the boundary |
title_full |
Difference factorizations and monotonicity in inverse medium scattering for contrasts with fixed sign on the boundary |
title_fullStr |
Difference factorizations and monotonicity in inverse medium scattering for contrasts with fixed sign on the boundary |
title_full_unstemmed |
Difference factorizations and monotonicity in inverse medium scattering for contrasts with fixed sign on the boundary |
title_sort |
Difference factorizations and monotonicity in inverse medium scattering for contrasts with fixed sign on the boundary |
author |
Lechleiter, Armin |
author_facet |
Lechleiter, Armin Lakshtanov, Evgeny |
author_role |
author |
author2 |
Lakshtanov, Evgeny |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Lechleiter, Armin Lakshtanov, Evgeny |
dc.subject.por.fl_str_mv |
Inverse scattering Factorization Monotonicity Characterization of boundary values |
topic |
Inverse scattering Factorization Monotonicity Characterization of boundary values |
description |
We generalize the factorization method for inverse medium scattering using a particular factorization of the difference of two far field operators. While the factorization method has been used so far mainly to identify the shape of a scatterer's support, we show that factorizations based on Dirichlet-to-Neumann operators can be used to compute bounds for numerical values of the medium on the boundary of its support. To this end, we generalize ideas from inside-outside duality to obtain a monotonicity principle that allows for alternative uniqueness proofs for particular inverse scattering problems (e.g., when obstacles are present inside the medium). This monotonicity principle indeed is our most important technical tool: It further directly shows that the boundary values of the medium's contrast function are uniquely determined by the corresponding far field operator. Our particular factorization of far field operators additionally implies that the factorization method rigorously characterizes the support of an inhomogeneous medium if the contrast function takes merely positive or negative values on the boundary of its support independently of the contrast's values inside its support. Finally, the monotonicity principle yields a simple algorithm to compute upper and lower bounds for these boundary values, assuming the support of the contrast is known. Numerical experiments show feasibility of a resulting numerical algorithm. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-11-04T15:31:37Z 2016-11-01T00:00:00Z 2016-11 |
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/10773/16247 |
url |
http://hdl.handle.net/10773/16247 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0036-1410 10.1137/16M1060819 |
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 |
Society for Industrial and Applied Mathematics |
publisher.none.fl_str_mv |
Society for Industrial and Applied Mathematics |
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 |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799137563709014016 |