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Inverse Scattering Theory and Transmission Eigenvalues (Paperback, 2nd Revised edition)
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Inverse Scattering Theory and Transmission Eigenvalues (Paperback, 2nd Revised edition)
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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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