Overview

Inverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. In the first edition of Inverse Scattering Theory and Transmission Eigenvalues, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. In particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers—a subset of transmission eigenvalues—using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles. 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.

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9781611977417

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Fioralba Cakoni is a Distinguished Professor in the Department of Mathematics at Rutgers University. She is coauthor with David Colton of A Qualitative Approach to Inverse Scattering Theory (Springer, 2014). David Colton is an Emeritus Unidel Professor in the Department of Mathematical Sciences at the University of Delaware. He is coauthor with Fioralba Cakoni of the aforementioned book and coauthor with Rainer Kress of Inverse Acoustic and Electromagnetic Scattering Theory (Springer, 2019). Houssem Haddar is a Director of Research at INRIA and is the scientific leader of the project team IDEFIX. He is coauthor with Ralph Hiptmair, Peter Monk, and Rodolfo Rodríguez of Computational Electromagnetism (Springer, 2015).

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