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

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. Review of earlier editions: “Colton and Kress have written a scholarly, state of the art account of their view of direct and inverse scattering. The book is a pleasure to read as a graduate text or to dip into at leisure. It suggests a number of open problems and will be a source of inspiration for many years to come.” SIAM Review, September 1994 “This book should be on the desk of any researcher, any student, any teacher interested in scattering theory.” Mathematical Intelligencer, June 1994

A comprehensive and updated overview of the theory, algorithms and applications of for electromagnetic inverse scattering problems Offers the recent and most important advances in inverse scattering grounded in fundamental theory, algorithms and practical engineering applications Covers the latest, most relevant inverse scattering techniques like signal subspace methods, time reversal, linear sampling, qualitative methods, compressive sensing, and noniterative methods Emphasizes theory, mathematical derivation and physical insights of various inverse scattering problems Written by a leading expert in the field

"Optimization and Regularization for Computational Inverse Problems and Applications" focuses on advances in inversion theory and recent developments with practical applications, particularly emphasizing the combination of optimization and regularization for solving inverse problems. This book covers both the methods, including standard regularization theory, Fejer processes for linear and nonlinear problems, the balancing principle, extrapolated regularization, nonstandard regularization, nonlinear gradient method, the nonmonotone gradient method, subspace method and Lie group method; and the practical applications, such as the reconstruction problem for inverse scattering, molecular spectra data processing, quantitative remote sensing inversion, seismic inversion using the Lie group method, and the gravitational lensing problem. Scientists, researchers and engineers, as well as graduate students engaged in applied mathematics, engineering, geophysics, medical science, image processing, remote sensing and atmospheric science will benefit from this book. Dr. Yanfei Wang is a Professor at the Institute of Geology and Geophysics, Chinese Academy of Sciences, China. Dr. Sc. Anatoly G. Yagola is a Professor and Assistant Dean of the Physical Faculty, Lomonosov Moscow State University, Russia. Dr. Changchun Yang is a Professor and Vice Director of the Institute of Geology and Geophysics, Chinese Academy of Sciences, China.

This book is the third volume of three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" taking place in Linz, Austria, October 3-7, 2011. This book surveys recent developments in the analysis of wave propagation problems. The topics covered include aspects of the forward problem and problems in inverse problems, as well as applications in the earth sciences. Wave propagation problems are ubiquitous in environmental applications such as seismic analysis, acoustic and electromagnetic scattering. The design of efficient numerical methods for the forward problem, in which the scattered field is computed from known geometric configurations is very challenging due to the multiscale nature of the problems. Even more challenging are inverse problems where material parameters and configurations have to be determined from measurements in conjunction with the forward problem. This book contains review articles covering several state-of-the-art numerical methods for both forward and inverse problems. This collection of survey articles focusses on the efficient computation of wave propagation and scattering is a core problem in numerical mathematics, which is currently of great research interest and is central to many applications in energy and the environment. Two generic applications which resonate strongly with the central aims of the Radon Special Semester 2011 are forward wave propagation in heterogeneous media and seismic inversion for subsurface imaging. As an example of the first application, modelling of absorption and scattering of radiation by clouds, aerosol and precipitation is used as a tool for interpretation of (e.g.) solar, infrared and radar measurements, and as a component in larger weather/climate prediction models in numerical weather forecasting. As an example of the second application, inverse problems in wave propagation in heterogeneous media arise in the problem of imaging the subsurface below land or marine deposits. The book records the achievements of Workshop 3 "Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment". It brings together key numerical mathematicians whose interest is in the analysis and computation of wave propagation and scattering problems, and in inverse problems, together with practitioners from engineering and industry whose interest is in the applications of these core problems.

The 'factorization method', discovered by Professor Kirsch, is a relatively new method for solving certain types of inverse scattering problems and problems in tomography. The text introduces the reader to this promising approach and discusses the wide applicability of this method by choosing typical examples.