A new approach to solve the inverse scattering problem for waves: combining the TRAC and the Adaptive Inversion methods.

Maya de Buhan (1) , Marie Kray (2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 Department of Mathematics [Basel]

The aim of this paper is to propose a new method to solve the inverse scattering problem. This method works directly in the time-dependent domain, using the wave equation and proceeds in two steps. The first step is the Time-Reversed Absorbing Condition ({\em TRAC}) method to reconstruct and regularize the signal and to reduce the computational domain. The second step is the Adaptive Inversion method to solve the inverse problem from the {\em TRAC} data, by using basis and mesh adaptation. This strategy allows to recover the position, the shape and the properties of the scatterer in a precise and robust manner.

Domaines: Analyse numérique [math.NA]

Maya de Buhan, Marie Kray. A new approach to solve the inverse scattering problem for waves: combining the TRAC and the Adaptive Inversion methods.. 2013. ⟨hal-00799110v1⟩