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Inverse Acoustic and Electromagnetic Scattering Theory, Second Edition (1998)
| Citations: | 1061 - 45 self |
BibTeX
@MISC{Colton98inverseacoustic,
author = {David Colton},
title = {Inverse Acoustic and Electromagnetic Scattering Theory, Second Edition},
year = {1998}
}
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Abstract
Abstract. This paper is a survey of the inverse scattering problem for time-harmonic acoustic and electromagnetic waves at fixed frequency. We begin by a discussion of “weak scattering ” and Newton-type methods for solving the inverse scattering problem for acoustic waves, including a brief discussion of Tikhonov’s method for the numerical solution of ill-posed problems. We then proceed to prove a uniqueness theorem for the inverse obstacle problems for acoustic waves and the linear sampling method for reconstructing the shape of a scattering obstacle from far field data. Included in our discussion is a description of Kirsch’s factorization method for solving this problem. We then turn our attention to uniqueness and reconstruction algorithms for determining the support of an inhomogeneous, anisotropic media from acoustic far field data. Our survey is concluded by a brief discussion of the inverse scattering problem for time-harmonic electromagnetic waves. 1.
Keyphrases
inverse scattering problem inverse acoustic second edition electromagnetic scattering theory brief discussion acoustic wave field data electromagnetic wave numerical solution uniqueness theorem linear sampling method time-harmonic electromagnetic wave ill-posed problem weak scattering kirsch factorization method reconstruction algorithm newton-type method inverse obstacle problem anisotropic medium fixed frequency
