On the identification of piecewise constant coefficients in optical diffusion tomography by level set

Autores
Agnelli, Juan Pablo; Cezaro, Adriano de; Leitão, Antonio; Alves, Maicon Marques
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Fil: Agnelli, Juan Pablo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.
Fil: Agnelli, Juan Pablo. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina.
Agnelli, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigación y Estudios de Matemática; Argentina.
Fil: Cezaro, Adriano de. Federal University of Rio Grande. Institute of Mathematics Statistics and Physics; Brazil.
Fil: Leitão, Antonio. Federal University of Santa Catarina. Department of Mathematics; Brazil.
Fil: Alves, Maicon Marques. Federal University of Santa Catarina. Department of Mathematics; Brazil.
In this paper, we propose a level set regularization approach combined with a split strategy for the simultaneous identification of piecewise constant diffusion and absorption coefficients from a finite set of optical tomography data (Neumann-to-Dirichlet data). This problem is a high nonlinear inverse problem combining together the exponential and mildly ill-posedness of diffusion and absorption coefficients, respectively. We prove that the parameter-to-measurement map satisfies sufficient conditions (continuity in the L1 topology) to guarantee regularization properties of the proposed level set approach. On the other hand, numerical tests considering different configurations bring new ideas on how to propose a convergent split strategy for the simultaneous identification of the coefficients. The behavior and performance of the proposed numerical strategy is illustrated with some numerical examples.
info:eu-repo/semantics/publishedVersion
Fil: Agnelli, Juan Pablo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.
Fil: Agnelli, Juan Pablo. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina.
Agnelli, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigación y Estudios de Matemática; Argentina.
Fil: Cezaro, Adriano de. Federal University of Rio Grande. Institute of Mathematics Statistics and Physics; Brazil.
Fil: Leitão, Antonio. Federal University of Santa Catarina. Department of Mathematics; Brazil.
Fil: Alves, Maicon Marques. Federal University of Santa Catarina. Department of Mathematics; Brazil.
Matemática Aplicada
Materia
Optical tomography
Parameter identification
Level set regularization
Numerical strategy
Nivel de accesibilidad
acceso abierto
Condiciones de uso
Repositorio
Repositorio Digital Universitario (UNC)
Institución
Universidad Nacional de Córdoba
OAI Identificador
oai:rdu.unc.edu.ar:11086/555032
Acceder
id RDUUNC_300083872a13c58a5e5bb64d078b8493
oai_identifier_str oai:rdu.unc.edu.ar:11086/555032
network_acronym_str RDUUNC
repository_id_str 2572
network_name_str Repositorio Digital Universitario (UNC)
spelling On the identification of piecewise constant coefficients in optical diffusion tomography by level setAgnelli, Juan PabloCezaro, Adriano deLeitão, AntonioAlves, Maicon MarquesOptical tomographyParameter identificationLevel set regularizationNumerical strategyFil: Agnelli, Juan Pablo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.Fil: Agnelli, Juan Pablo. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina.Agnelli, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigación y Estudios de Matemática; Argentina.Fil: Cezaro, Adriano de. Federal University of Rio Grande. Institute of Mathematics Statistics and Physics; Brazil.Fil: Leitão, Antonio. Federal University of Santa Catarina. Department of Mathematics; Brazil.Fil: Alves, Maicon Marques. Federal University of Santa Catarina. Department of Mathematics; Brazil.In this paper, we propose a level set regularization approach combined with a split strategy for the simultaneous identification of piecewise constant diffusion and absorption coefficients from a finite set of optical tomography data (Neumann-to-Dirichlet data). This problem is a high nonlinear inverse problem combining together the exponential and mildly ill-posedness of diffusion and absorption coefficients, respectively. We prove that the parameter-to-measurement map satisfies sufficient conditions (continuity in the L1 topology) to guarantee regularization properties of the proposed level set approach. On the other hand, numerical tests considering different configurations bring new ideas on how to propose a convergent split strategy for the simultaneous identification of the coefficients. The behavior and performance of the proposed numerical strategy is illustrated with some numerical examples.info:eu-repo/semantics/publishedVersionFil: Agnelli, Juan Pablo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.Fil: Agnelli, Juan Pablo. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina.Agnelli, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigación y Estudios de Matemática; Argentina.Fil: Cezaro, Adriano de. Federal University of Rio Grande. Institute of Mathematics Statistics and Physics; Brazil.Fil: Leitão, Antonio. Federal University of Santa Catarina. Department of Mathematics; Brazil.Fil: Alves, Maicon Marques. Federal University of Santa Catarina. Department of Mathematics; Brazil.Matemática Aplicadahttps://orcid.org/0000-0001-7982-6793https://orcid.org/0000-0001-8431-9120https://orcid.org/0000-0001-6785-8835https://orcid.org/0000-0001-5734-69592017info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfAgnelli, J. P., Cezaro, A. de, Leitão, A. y Alves, M. M. (2017). On the identification of piecewise constant coefficients in optical diffusion tomography by level set. ESAIM: Control, Optimisation and Calculus of Variations, 23 (2), 663-683. https://doi.org/10.1051/cocv/20160071292-8119http://hdl.handle.net/11086/5550321262-3377https://doi.org/10.1051/cocv/2016007enginfo:eu-repo/semantics/openAccessreponame:Repositorio Digital Universitario (UNC)instname:Universidad Nacional de Córdobainstacron:UNC2025-09-04T12:31:16Zoai:rdu.unc.edu.ar:11086/555032Institucionalhttps://rdu.unc.edu.ar/Universidad públicaNo correspondehttp://rdu.unc.edu.ar/oai/snrdoca.unc@gmail.comArgentinaNo correspondeNo correspondeNo correspondeopendoar:25722025-09-04 12:31:16.261Repositorio Digital Universitario (UNC) - Universidad Nacional de Córdobafalse
dc.title.none.fl_str_mv On the identification of piecewise constant coefficients in optical diffusion tomography by level set
title On the identification of piecewise constant coefficients in optical diffusion tomography by level set
spellingShingle On the identification of piecewise constant coefficients in optical diffusion tomography by level set
Agnelli, Juan Pablo
Optical tomography
Parameter identification
Level set regularization
Numerical strategy
title_short On the identification of piecewise constant coefficients in optical diffusion tomography by level set
title_full On the identification of piecewise constant coefficients in optical diffusion tomography by level set
title_fullStr On the identification of piecewise constant coefficients in optical diffusion tomography by level set
title_full_unstemmed On the identification of piecewise constant coefficients in optical diffusion tomography by level set
title_sort On the identification of piecewise constant coefficients in optical diffusion tomography by level set
dc.creator.none.fl_str_mv Agnelli, Juan Pablo
Cezaro, Adriano de
Leitão, Antonio
Alves, Maicon Marques
author Agnelli, Juan Pablo
author_facet Agnelli, Juan Pablo
Cezaro, Adriano de
Leitão, Antonio
Alves, Maicon Marques
author_role author
author2 Cezaro, Adriano de
Leitão, Antonio
Alves, Maicon Marques
author2_role author
author
author
dc.contributor.none.fl_str_mv https://orcid.org/0000-0001-7982-6793
https://orcid.org/0000-0001-8431-9120
https://orcid.org/0000-0001-6785-8835
https://orcid.org/0000-0001-5734-6959
dc.subject.none.fl_str_mv Optical tomography
Parameter identification
Level set regularization
Numerical strategy
topic Optical tomography
Parameter identification
Level set regularization
Numerical strategy
dc.description.none.fl_txt_mv Fil: Agnelli, Juan Pablo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.
Fil: Agnelli, Juan Pablo. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina.
Agnelli, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigación y Estudios de Matemática; Argentina.
Fil: Cezaro, Adriano de. Federal University of Rio Grande. Institute of Mathematics Statistics and Physics; Brazil.
Fil: Leitão, Antonio. Federal University of Santa Catarina. Department of Mathematics; Brazil.
Fil: Alves, Maicon Marques. Federal University of Santa Catarina. Department of Mathematics; Brazil.
In this paper, we propose a level set regularization approach combined with a split strategy for the simultaneous identification of piecewise constant diffusion and absorption coefficients from a finite set of optical tomography data (Neumann-to-Dirichlet data). This problem is a high nonlinear inverse problem combining together the exponential and mildly ill-posedness of diffusion and absorption coefficients, respectively. We prove that the parameter-to-measurement map satisfies sufficient conditions (continuity in the L1 topology) to guarantee regularization properties of the proposed level set approach. On the other hand, numerical tests considering different configurations bring new ideas on how to propose a convergent split strategy for the simultaneous identification of the coefficients. The behavior and performance of the proposed numerical strategy is illustrated with some numerical examples.
info:eu-repo/semantics/publishedVersion
Fil: Agnelli, Juan Pablo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.
Fil: Agnelli, Juan Pablo. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina.
Agnelli, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigación y Estudios de Matemática; Argentina.
Fil: Cezaro, Adriano de. Federal University of Rio Grande. Institute of Mathematics Statistics and Physics; Brazil.
Fil: Leitão, Antonio. Federal University of Santa Catarina. Department of Mathematics; Brazil.
Fil: Alves, Maicon Marques. Federal University of Santa Catarina. Department of Mathematics; Brazil.
Matemática Aplicada
description Fil: Agnelli, Juan Pablo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.
publishDate 2017
dc.date.none.fl_str_mv 2017
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
status_str publishedVersion
format article
dc.identifier.none.fl_str_mv Agnelli, J. P., Cezaro, A. de, Leitão, A. y Alves, M. M. (2017). On the identification of piecewise constant coefficients in optical diffusion tomography by level set. ESAIM: Control, Optimisation and Calculus of Variations, 23 (2), 663-683. https://doi.org/10.1051/cocv/2016007
1292-8119
http://hdl.handle.net/11086/555032
1262-3377
https://doi.org/10.1051/cocv/2016007
identifier_str_mv Agnelli, J. P., Cezaro, A. de, Leitão, A. y Alves, M. M. (2017). On the identification of piecewise constant coefficients in optical diffusion tomography by level set. ESAIM: Control, Optimisation and Calculus of Variations, 23 (2), 663-683. https://doi.org/10.1051/cocv/2016007
1292-8119
1262-3377
url http://hdl.handle.net/11086/555032
https://doi.org/10.1051/cocv/2016007
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositorio Digital Universitario (UNC)
instname:Universidad Nacional de Córdoba
instacron:UNC
reponame_str Repositorio Digital Universitario (UNC)
collection Repositorio Digital Universitario (UNC)
instname_str Universidad Nacional de Córdoba
instacron_str UNC
institution UNC
repository.name.fl_str_mv Repositorio Digital Universitario (UNC) - Universidad Nacional de Córdoba
repository.mail.fl_str_mv oca.unc@gmail.com
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score 13.13397

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