The Factorization Method for Inverse Problems

by Andreas Kirsch, Natalia Grinberg

Overview

The factorization method is a relatively new method for solving certain types of inverse scattering problems in tomography. Aimed at students and researchers in Applied Mathematics, Physics, and Engineering, this text introduces the reader to this promising approach for solving important classes of inverse problems. The wide applicability of this method is discussed by choosing typical examples, such as inverse scattering problems for the scalar Helmholtz equation, a scattering problem for Maxwell's equation, and a problem in impedance and optical tomography. The last section of the book compares the Factorization Method to established sampling methods (the Linear Sampling Method, the Singular Method, and the Probe Method)

Product Details

ISBN-13:	9780199213535
Publisher:	Oxford University Press
Publication date:	02/09/2008
Series:	Oxford Lecture Series in Mathematics and Its Applications , #36
Pages:	216
Product dimensions:	9.30(w) x 6.00(h) x 0.80(d)

Table of Contents

PrefaceChapter 1. The Simplest Cases: Dirichlet and Neumann Boundary ConditionsChapter 2. The Factorization Method for Other Types of Inverse Obstacle Scattering ProblemsChapter 3. The Mixed Boundary Value ProblemChapter 4. The MUSIC Algorithm and Scattering by an Inhomogeneous MethodChapter 5. The Factorization method for Maxwell's EquationsChapter 6. The Factorization Method in Impedance TomographyChapter 7. Alternative Sampling and Probe MethodsBibliography

Editorial Reviews

"This is a nice collection of results on the factorization method for a variety of scattering applications. It provides beginning researchers with a good survey of the basic theoretical approach, and for more experienced researchers working with factorization techniques it is a good reference source. I await the second edition with great anticipation."—SIAM Review

From the Publisher