Some Reconstruction Methods for Inverse Scattering Problems

Abstract

Inverse scattering problems are one of the main research areas in the optimization techniques. The main purpose of inverse scattering problems is to detect the physical properties of an obstacle from some information related to the scattered waves of the obstacle for given incident wave. Generally, if the incident plane waves are given from the finite number of directions, which are indeed the practical situations, there is no uniqueness for reconstructing the obstacle properties such as the boundary shape. In these cases, the optimization techniques can be applied to reconstructing the obstacle approximately. That is, the obstacle shape is approximated by a minimizer of some cost functional which measures the defect between the measurement data of the scattered wave and the computational scattered wave related to the approximate obstacle. Of course, for this optimization problems in infinite dimensional space, some regularizing term should be introduced to the cost functional.