Colton D., Kress R. Inverse Acoustic and Electromagnetic Scattering Theory

3rd edition. — Springer, 2012. — 405 p.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.The Helmholtz Equation.
Direct Acoustic Obstacle Scattering.
Ill-Posed Problems.
Inverse Acoustic Obstacle Scattering.
The Maxwell Equations.
Inverse Electromagnetic Obstacle Scattering.
Acoustic Waves in an Inhomogeneous Medium.
Electromagnetic Waves in an Inhomogeneous Medium.
The Inverse Medium Problem.