Point Sources and Multipoles in Inverse Scattering Theory: 1st Edition (Paperback) book cover

Point Sources and Multipoles in Inverse Scattering Theory

1st Edition

By Roland Potthast

Chapman and Hall/CRC

302 pages

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Paperback: 9781584882527
pub: 2001-05-30
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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.

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

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

About the Series

Chapman & Hall/CRC Research Notes in Mathematics Series

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Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations
SCI040000
SCIENCE / Mathematical Physics