New characterizations of solutions in inverse scattering theory

Abstract

This paper introduces a new approach to characterize the shape ω of a scattering medium (either an acoustically soft obstacle or an inhomogeneous medium) by the far field data. In contrast to the Linear Sampling Method normality of the far field operator is not needed. Therefore, also scattering by limited far field data and absorbing media can be treated. While in the Linear Sampling Method the points in the interior of ω are characterized by the solution of an integral equation of the first kind, for our new method a constrained optimization problem has to be solved. Although this new approach is more time consuming some numerical experiments at the end of this paper show the practicability of the method.

Keywords:

• Inverse problems
• scattering theory
• far field operator
• Lippman-Schwinger equation
• optimization problem

AMS:

• 35P25
• 35R30
• 35J05