The Fixed Angle Inverse Scattering Problem

Abstract

The speaker and his collaborator consider the fixed angle inverse scattering problem for potentials in Euclidean space. The main result shows that a compactly supported potential is uniquely determined by its scattering amplitude for two opposite fixed angles. They also show that potentials having a generalized reflection symmetry are uniquely determined by their fixed angle scattering data. The proofs are based on reducing the inverse scattering problem to a unique continuation type problem for the wave equation in the spirit of the Bukhgeim-Klibanov method, and on using suitable Carleman estimates.

This is a joint work with Rakesh (Delaware).

About the speaker

Prof. Mikko Salo received his MS in Mathematics from the University of Oulu in 2001 and his PhD in Applied Mathematics from the University of Helsinki in 2004. He continued his research as a Postdoctoral Researcher at the University of Helsinki in 2005-2008 and as an Academy Research Fellow at the University of Helsinki and the University of Jyväskylä in 2008-2013. Since 2013, he has become a Professor in the Department of Mathematics at the University of Jyväskylä.

Prof. Salo’s work is in mathematical analysis, geometry and applications. His research group focuses on fundamental theoretical aspects of inverse problems such as the Calderón problem in electrical imaging and travel time tomography in seismic imaging. He is the Managing Editor of Inverse Problems and Imaging and the Editor of Mathematica Scandinavica.

Prof. Salo is the recipient of the 2012 MediaV Young Researcher Award at the International Conference on Inverse Problems, the 2013 Calderón Prize of the Inverse Problems International Association and the 2014 Väisälä Prize of the Finnish Academy of Science and Letters.

About the program

For more information, please refer to the program website at http://iasprogram.ust.hk/inverseproblems.