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

Fil: Agnelli, Juan Pablo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.

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Detalles Bibliográficos
Autores principales: Agnelli, Juan Pablo, Cezaro, Adriano de, Leitão, Antonio, Alves, Maicon Marques
Otros Autores: https://orcid.org/0000-0001-7982-6793
Formato: publishedVersion article
Lenguaje:Inglés
Publicado: 2025
Materias:
Optical tomography
Parameter identification
Level set regularization
Numerical strategy
Acceso en línea:http://hdl.handle.net/11086/555032
https://doi.org/10.1051/cocv/2016007
Aporte de:
Repositorio Digital Universitario (UNC) de Universidad Nacional de Córdoba
id I10-R141-11086-555032
record_format dspace
spelling I10-R141-11086-5550322025-03-12T14:50:57Z On the identification of piecewise constant coefficients in optical diffusion tomography by level set Agnelli, Juan Pablo Cezaro, Adriano de Leitão, Antonio Alves, Maicon Marques 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 Optical tomography Parameter identification Level set regularization Numerical strategy 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. 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 2025-03-05T14:30:32Z 2025-03-05T14:30:32Z 2017 article 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 eng Atribución/Reconocimiento-NoComercial-SinDerivados 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/deed.es Impreso; Electrónico y/o Digital
institution Universidad Nacional de Córdoba
institution_str I-10
repository_str R-141
collection Repositorio Digital Universitario (UNC)
language Inglés
topic Optical tomography
Parameter identification
Level set regularization
Numerical strategy
spellingShingle Optical tomography
Parameter identification
Level set regularization
Numerical strategy
Agnelli, Juan Pablo
Cezaro, Adriano de
Leitão, Antonio
Alves, Maicon Marques
On the identification of piecewise constant coefficients in optical diffusion tomography by level set
topic_facet Optical tomography
Parameter identification
Level set regularization
Numerical strategy
description Fil: Agnelli, Juan Pablo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.
author2 https://orcid.org/0000-0001-7982-6793
author_facet https://orcid.org/0000-0001-7982-6793
Agnelli, Juan Pablo
Cezaro, Adriano de
Leitão, Antonio
Alves, Maicon Marques
format publishedVersion
article
author Agnelli, Juan Pablo
Cezaro, Adriano de
Leitão, Antonio
Alves, Maicon Marques
author_sort Agnelli, Juan Pablo
title On the identification of piecewise constant coefficients in optical diffusion tomography by level set
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
publishDate 2025
url http://hdl.handle.net/11086/555032
https://doi.org/10.1051/cocv/2016007
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