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Preprints, Working Papers, ... Year : 2021

Source and metric estimation in the eikonal equation using optimization on a manifold

Abstract

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.
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Dates and versions

hal-03475139 , version 1 (10-12-2021)

Identifiers

  • HAL Id : hal-03475139 , version 1

Cite

Jérôme Fehrenbach, Lisl Weynans. Source and metric estimation in the eikonal equation using optimization on a manifold. 2021. ⟨hal-03475139⟩
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