Inverse Scattering Theory and Transmission Eigenvalues CBMS-NSF Regional Conference Series in Applied Mathematics Series

Inverse scattering theory is a major theme of applied mathematics, and has applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is nonlinear and ill-posed, thus presenting particular problems in the development of efficient inversion algorithms. Initial efforts to address these problems focused on nonlinear optimization methods, which required strong a priori information. This led to a qualitative approach to inverse scattering theory in which the amount of a priori information is drastically reduced, although at the expense of only obtaining limited information about the values of constitutive parameters. This book provides an introduction to this important new direction in inverse scattering theory. Beginning with a basic introduction to the theory, the authors proceed to more recent developments, including a detailed discussion of the transmission eigenvalue problem. Both the new generalized linear sampling method and well-known linear sampling and factorization methods are included.

Preface; 1. Inverse scattering theory; 2. The determination of the support of inhomogeneous media; 3. The interior transmission problem; 4. The existence of transmission eigenvalues; 5. Inverse spectral problems for transmission eigenvalues; Bibliography; Index.

Fioralba Cakoni is a professor in the Department of Mathematics at Rutgers University, New Jersey. She is coauthor of A Qualitative Approach to Inverse Scattering Theory (with David Colton, 2014).
David Colton is a professor in the Department of Mathematical Sciences at the University of Delaware, where he was appointed Unidel Professor in 1996. He is coauthor of A Qualitative Approach to Inverse Scattering Theory (with Fioralba Cakoni, 2014) and Inverse Acoustic and Electromagnetic Scattering Theory, 3rd edition (with Rainer Kress, 2013).
Houssem Haddar is Director of Research at the Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt and a part-time Professor at École Polytechnique, Paris. He is a coauthor of Computational Electromagnetism (with with Ralf Hiptmair, Peter Monk and Rodolfo Rodriguez, 2015).