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.
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | info:eu-repo/semantics/publishedVersion |
| Language: | eng |
| Published: |
2025
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| Subjects: | |
| Online Access: | http://hdl.handle.net/11086/555032 https://doi.org/10.1051/cocv/2016007 |
| _version_ | 1826514568006860800 |
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| author | Agnelli, Juan Pablo Cezaro, Adriano de Leitão, Antonio Alves, Maicon Marques |
| 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 |
| author_sort | Agnelli, Juan Pablo |
| collection | Repositorio Digital Universitario |
| description | Fil: Agnelli, Juan Pablo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina. |
| format | info:eu-repo/semantics/publishedVersion |
| id | rdu-unc.555032 |
| institution | Universidad Nacional de Cordoba |
| language | eng |
| publishDate | 2025 |
| record_format | dspace |
| spelling | rdu-unc.5550322025-03-05T15:07:04Z 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 |
| 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 |
| title | 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_short | 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 |
| topic | Optical tomography Parameter identification Level set regularization Numerical strategy |
| url | http://hdl.handle.net/11086/555032 https://doi.org/10.1051/cocv/2016007 |
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