Point Sources and Multipoles in Inverse Scattering Theory  book cover
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Point Sources and Multipoles in Inverse Scattering Theory





ISBN 9781584882527
Published May 30, 2001 by Chapman and Hall/CRC
302 Pages

 
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Book Description

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. The study of inverse scattering, in particular, has developed rapidly with the ability to perform computational simulations of scattering processes and led to remarkable advances in a range of applications, from medical imaging and radar to remote sensing and seismic exploration.

Point Sources and Multipoles in Inverse Scattering Theory provides a survey of recent developments in inverse acoustic and electromagnetic scattering theory. Focusing on methods developed over the last six years by Colton, Kirsch, and the author, this treatment uses point sources combined with several far-reaching techniques to obtain qualitative reconstruction methods. The author addresses questions of uniqueness, stability, and reconstructions for both two-and three-dimensional problems.

With interest in extracting information about an object through scattered waves at an all-time high, Point Sources and Multipoles in Inverse Scattering Theory provides a valuable source of information from both the mathematical and applications perspectives. It offers insight into the general recovery of information from incomplete data and has direct, practical relevance to work on image reconstruction.

Table of Contents

INTRODUCTION AND TOOLS
A Survey About Inverse Scattering Theory
Basic Definitions and Tools
DIRECT SCATTERING PROBLEMS
Acoustic Obstacle Scattering
The Inhomogeneous Acoustic Medium
Electromagnetic Scattering by a Perfect Conductor
The Electromagnetic Inhomogeneous Medium
Scattering by Orthotropic Media
Anisotropic Electromagnetic Media
UNIQUENESS AND STABILITY IN INVERSE SCATTERING
Acoustic Scattering
Electromagnetic Scattering
THE CASE OF FINITE DATA
Finite Data in Inverse Acoustic Scattering
Inverse Electromagnetic Scattering
THE POINT-SOURCE METHOD AND APPLICATIONS
Reconstruction Of Acoustic Scatters
Inverse Electromagnetic Scattering
Reconstruction of the Boundary Values of Scattered Fields
Convergence of a Regularized Newton Method
SINGULAR SOURCES AND SHAPE RECONSTRUCTION
Acoustic Scattering
Electromagnetic Scattering
LINEAR SAMPLING METHODS
The Original Linear Sampling Method
Spectral Theory and a Modified Linear Sampling Method
Shape Reconstruction for Orthotropic Media
Anisotropic Electromagnetic Media
REFERENCES
INDEX

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Reviews

"The presentation…is sound and fresh…provides valuable sources of information from both the mathematical and applications perspectives…will prove particularly useful to engineers in acoustics, antennas and remote sensing as well as to students and researchers in electromagnetic theory, scattering theory, and partial differential equations."
-Vladislav G. Dubrovsky in Mathematical Reviews