On the Mathematical Basis of the Linear Sampling Method

Date
2002
Authors
Cakoni, Fioralba
Colton, David
Journal Title
Journal ISSN
Volume Title
Publisher
Department of Mathematical Sciences
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.
Description
Keywords
inverse scattering , mixed boundary conditions , linear sampling method , inhomogeneous media
Citation