Source and metric estimation in the eikonal equation using optimization on a manifold
| hal.structure.identifier | Institut de Mathématiques de Toulouse UMR5219 [IMT] | |
| dc.contributor.author | FEHRENBACH, Jérôme | |
| hal.structure.identifier | Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | WEYNANS, Lisl | |
| dc.date.accessioned | 2024-04-04T02:43:28Z | |
| dc.date.available | 2024-04-04T02:43:28Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191339 | |
| dc.description.abstractEn | We address the estimation of the source(s) location in the eikonal equation on a Riemann surface, as well as the determination of the metric when it depends on a few parameters. The available observations are the arrival times or are obtained indirectly from the arrival times by an observation operator, this frame is intended to describe electro-cardiographic imaging. The sensitivity of the arrival times is computed from Log x the log map wrt to the source x on the surface. The Log x map is approximated by solving an elliptic vectorial equation, using the Vector Heat Method. The L 2-error function between the model predictions and the observations is minimized using Gauss-Newton optimization on the Riemann surface. This allows to obtain fast convergence. We present numerical results, where coefficients describing the metric are also recovered like anisotropy and global orientation. | |
| dc.language.iso | en | |
| dc.subject.en | Inverse problem | |
| dc.subject.en | electrocardiographic imaging | |
| dc.subject.en | eikonal equation | |
| dc.title.en | Source and metric estimation in the eikonal equation using optimization on a manifold | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-03475139 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03475139v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=FEHRENBACH,%20J%C3%A9r%C3%B4me&WEYNANS,%20Lisl&rft.genre=preprint |
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