The Linear Sampling Method in Inverse Electromagnetic Scattering (CBMS-NSF Regional Conference Series in Applied Mathematics)

The linear sampling method is the oldest and most developed of the qualitative methods in inverse scattering theory. It is based on solving a linear integral equation and then using the equation s solution as an indicator function for the determination of the support of the scattering object. This book describes the linear sampling method for a variety of electromagnetic scattering problems. It presents uniqueness theorems and the derivation of various inequalities on the material properties of the scattering object from a knowledge of the far field pattern of the scattered wave.

Also covered are the approximation properties of Herglotz wave functions; the behavior of solutions to the interior transmission problem, a novel interior boundary value problem; and numerical examples of the inversion scheme.

Audience: This book is intended for mathematicians and engineers performing research in inverse electromagnetic scattering theory. It is also appropriate for an advanced graduate course on inverse problems.

Contents: Preface; Chapter 1: Inverse Scattering in Two Dimensions; Chapter 2: Maxwell s Equations; Chapter 3: The Inverse Problem for Obstacles; Chapter 4: The Inverse Scattering Problem for Anisotropic Media; Chapter 5: The Inverse Scattering Problem for Thin Objects; Chapter 6: The Inverse Scattering Problem for Buried Objects; Bibliography; Index.