An optimal quasi solution for the cauchy problem for laplace equation in the framework of inverse ECG
| hal.structure.identifier | Facultad de Ciencias Físico Matemáticas [Puebla] [FCFM BUAP] | |
| dc.contributor.author | HERNÁNDEZ-MONTERO, Eduardo | |
| hal.structure.identifier | Facultad de Ciencias Físico Matemáticas [Puebla] [FCFM BUAP] | |
| dc.contributor.author | FRAGUELA-COLLAR, Andrés | |
| hal.structure.identifier | Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN] | |
| dc.contributor.author | HENRY, Jacques | |
| dc.date | 2018 | |
| dc.date.accessioned | 2024-04-04T03:03:58Z | |
| dc.date.available | 2024-04-04T03:03:58Z | |
| dc.date.issued | 2018 | |
| dc.identifier.issn | 0973-5348 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193112 | |
| dc.description.abstractEn | The inverse ECG problem is set as a boundary data completion for the Laplace equation: at each time the potential is measured on the torso and its normal derivative is null. One aims at reconstructing the potential on the heart. A new regularization scheme is applied to obtain an optimal regularization strategy for the boundary data completion problem. We consider the R n+1 domain Ω. The piecewise regular boundary of Ω is defined as the union ∂Ω = Γ1 ∪ Γ0 ∪ Σ, where Γ1 and Γ0 are disjoint, regular, and n-dimensional surfaces. Cauchy boundary data is given in Γ0, and null Dirichlet data in Σ, while no data is given in Γ1. This scheme is based on two concepts: admissible output data for an ill-posed inverse problem, and the conditionally well-posed approach of an inverse problem. An admissible data is the Cauchy data in Γ0 corresponding to an harmonic function in C 2 (Ω) ∩ H 1 (Ω). The methodology roughly consists of first characterizing the admissible Cauchy data, then finding the minimum distance projection in the L 2-norm from the measured Cauchy data to the subset of admissible data characterized by given a priori information, and finally solving the Cauchy problem with the aforementioned projection instead of the original measurement. | |
| dc.language.iso | en | |
| dc.publisher | EDP Sciences | |
| dc.subject.en | Optimal regularization | |
| dc.subject.en | Quasi solution | |
| dc.subject.en | Invariant embedding | |
| dc.subject.en | Cauchy problem | |
| dc.subject.en | Factorization method | |
| dc.subject.en | ECG inverse problem | |
| dc.title.en | An optimal quasi solution for the cauchy problem for laplace equation in the framework of inverse ECG | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1051/mmnp/2018062 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Sciences du Vivant [q-bio] | |
| dc.subject.hal | Sciences du Vivant [q-bio]/Médecine humaine et pathologie | |
| bordeaux.journal | Mathematical Modelling of Natural Phenomena | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01933948 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01933948v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematical%20Modelling%20of%20Natural%20Phenomena&rft.date=2018&rft.eissn=0973-5348&rft.issn=0973-5348&rft.au=HERN%C3%81NDEZ-MONTERO,%20Eduardo&FRAGUELA-COLLAR,%20Andr%C3%A9s&HENRY,%20Jacques&rft.genre=article |
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