Using eigenvalues to detect anomalies in the exterior of a cavity

Abstract

We use modified near field operators and the generalized linear sampling method to investigate an inverse scattering problem for anisotropic media with data measured inside a cavity. The aim of this paper is to determine information on possible changes in the material properties of the surrounding medium under the assumption that the shape is known, and this will be accomplished by the introduction of a new class of eigenvalue problems for which the eigenvalues can be determined from the measured scattering data.