Inverse scattering theory has been a particularly active and successful field in applied mathematics and engineering for the past twenty years. The increasing demands of imaging and target identification require new powerful and flexible techniques besides the existing weak scattering approximation or nonlinear optimization methods. 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. It is accessible also to readers who are not professional mathematicians, thus making these new mathematical ideas in inverse scattering theory available to the wider scientific and engineering community.
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.
Note that E i can be written as E'o) I Ee(x,xo,p,ks)+ Ego). (6.3) where E; : Els7(-, x0, p) is the electric scattered field due to the background medium. The Green's function E i :: E i(x,x0, p) satisfies the Silver—Muller radiation ...
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.
6 Agarwal, K., Chen, X., and Zhong, Y. (2010) A multipole-expansion based linear sampling method for solving inverse scattering problems. Opt. Express, 18 (6), 6366–6381. 7 Cakoni, F. and Colton, D.L. (2014) A qualitative approach to ...
[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.
This book highlights the latest developments on the numerical methods for inverse scattering problems associated with acoustic, electromagnetic, and elastic waves.
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 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 ...
Authored by two experts in the field who have been long-time collaborators, this monograph treats the scattering and inverse scattering problems for the matrix Schrödinger equation on the half line with the general selfadjoint boundary ...
This book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics.