New numerical results for the Gel'fand-Calderon problem.


Séminaire Modèles et Algorithmes Déterministes: EDP-MOISE-MGMI

30/04/2015 - 15:30 Mr Matteo Santacesaria (University of Helsinki) Salle 1 - Tour IRMA

In this talk we present new numerical reconstruction results for the Gel'fand-Calderon inverse problem in two dimensions. This is the problem of the recovery of a potential in the Schrodinger equation from boundary data (Dirichlet-to-Neumann map) at fixed energy. Practical applications include ocean acoustic tomography and seismic imaging. We will review global uniqueness, reconstruction and stability results, and in particular the Lipschitz stable approximate reconstruction algorithm developed in collaboration with R. Novikov. The numerical results are obtained with this algorithm, and they clearly show how the resolution increases with the energy. The algorithm is based on the theory of inverse quantum scattering, a topic which will also be covered in the talk. This is a joint work with S. Siltanen and M. Lassas.