The inverse scattering problem is central to many areas of science and technology such as radar and sonar, medical imaging, geophysical exploration and nondestructive testing. This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. In this third edition, new sections have been added on the linear sampling and factorization methods for solving the inverse scattering problem as well as expanded treatments of iteration methods and uniqueness theorems for the inverse obstacle problem. These additions have in turn required an expanded presentation of both transmission eigenvalues and boundary integral equations in Sobolev spaces. As in the previous editions, emphasis has been given to simplicity over generality thus providing the reader with an accessible introduction to the field of inverse scattering theory.
Author(s): David Colton, Rainer Kress
Edition: 4
Publisher: Springer
Year: 2019
Language: English
Pages: 526
City: Switzerland AG
Front Matter ....Pages i-xvii
Introduction (David Colton, Rainer Kress)....Pages 1-13
The Helmholtz Equation (David Colton, Rainer Kress)....Pages 15-42
Direct Acoustic Obstacle Scattering (David Colton, Rainer Kress)....Pages 43-110
Ill-Posed Problems (David Colton, Rainer Kress)....Pages 111-136
Inverse Acoustic Obstacle Scattering (David Colton, Rainer Kress)....Pages 137-217
The Maxwell Equations (David Colton, Rainer Kress)....Pages 219-272
Inverse Electromagnetic Obstacle Scattering (David Colton, Rainer Kress)....Pages 273-302
Acoustic Waves in an Inhomogeneous Medium (David Colton, Rainer Kress)....Pages 303-344
Electromagnetic Waves in an Inhomogeneous Medium (David Colton, Rainer Kress)....Pages 345-369
Transmission Eigenvalues (David Colton, Rainer Kress)....Pages 371-437
The Inverse Medium Problem (David Colton, Rainer Kress)....Pages 439-495
Back Matter ....Pages 497-518
