On the Mathematical Basis of the Linear Sampling Method

Abstract

The linear sampling method is an algorithm for solving the inverse scattering problem for acoustic and electromagnetic waves. There are two versions of the linear sampling method. Although the second version is on a firm mathematical foundation, it is restricted to the case of non-absorbing media, full aperture scattering data or, more specifically, to the cases when the far field operator is normal. The first version of the linear sampling method is more flexible, being able to treat the aforementioned cases as well as partially coated obstacles. However, its mathematical foundation is less well established. In this paper we provide arguments giving a mathematical justification of the first version of the linear sampling method.