On the Mathematical Basis of the Linear Sampling Method
Date
2002
Authors
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