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.
[27] Colton, D., and Kirsch, A.: Karp's theorem in acoustic scattering theory. Proc. Amer. Math. Soc. 103,783–788 (1988). [28] Colton, D., and Kirsch, A.: An approximation problem in inverse scattering theory.
... we have by the Cartwright–Levinson theorem that in addition to the infinite set of positive zeros there exist an infinite ... Then the transmission eigenvalue problem is Δw + k ( 2 n1(r)+ i n2k(r) ) w = 0, 0 ≤ |x| < 1, Δv +k2v = 0, ...
Inverse Acoustic and Electromagnetic Scattering Theory
This classic book provides a rigorous treatment of the Riesz?Fredholm theory of compact operators in dual systems, followed by a derivation of the jump relations and mapping properties of scalar and vector potentials in spaces of continuous ...
This book is designed to be an introduction to this new approach in inverse scattering theory focusing on the use of sampling methods and transmission eigenvalues.
A comprehensive and updated overview of the theory, algorithms and applications of for electromagnetic inverse scattering problems Offers the recent and most important advances in inverse scattering grounded in fundamental theory, ...
Over the last twenty years, the growing availability of computing power has had an enormous impact on the classical fields of direct and inverse scattering.
This qualitative approach (the linear sampling method, the factorization method, the theory of transmission eigenvalues, etc.) is the theme of Inverse Scattering Theory and Transmission Eigenvalues.
This volume contains twelve survey papers about solution methods for inverse and ill-posed problems and about their application to specific types of inverse problems, e.g., in scattering theory, in tomography and medical applications, in ...
One class of such methods comes under the general description of qualitative methods in inverse scattering theory. This textbook is an easily-accessible "class-tested" introduction to the field.