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

4th Edition. — Springer, 2019. — 526 p. — (Applied Mathematical Sciences 93). — ISBN: 978-3-030-30350-1.The inverse scattering problem is central to many areas of science and technology such as radar, 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 fourth edition, a number of significant additions have been made including a new chapter on transmission eigenvalues and a new section on the impedance boundary condition where particular attention has been made to the generalized impedance boundary condition and to nonlocal impedance boundary conditions. Brief discussions on the generalized linear sampling method, the method of recursive linearization, anisotropic media and the use of target signatures in inverse scattering theory have also been added.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
Transmission Eigenvalues
The Inverse Medium Problem