Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.

Here is a clearly written introduction to three central areas of inverse problems: inverse problems in electromagnetic scattering theory, inverse spectral theory, and inverse problems in quantum scattering theory. Inverse problems, one of the most attractive parts of applied mathematics, attempt to obtain information about structures by nondestructive measurements. Based on a series of lectures presented by three of the authors, all experts in the field, the book provides a quick and easy way for readers to become familiar with the area through a survey of recent developments in inverse spectral and inverse scattering problems.

This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography. The aim of this book is twofold: in the first part, the reader is exposed to the basic notions and difficulties encountered with ill-posed problems. Basic properties of regularization methods for linear ill-posed problems are studied by means of several simple analytical and numerical examples. The second part of the book presents two special nonlinear inverse problems in detail - the inverse spectral problem and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness and continuous dependence on parameters. Then some theoretical results as well as numerical procedures for the inverse problems are discussed. The choice of material and its presentation in the book are new, thus making it particularly suitable for graduate students. Basic knowledge of real analysis is assumed. In this new edition, the Factorization Method is included as one of the prominent members in this monograph. Since the Factorization Method is particularly simple for the problem of EIT and this field has attracted a lot of attention during the past decade a chapter on EIT has been added in this monograph as Chapter 5 while the chapter on inverse scattering theory is now Chapter 6.The main changes of this second edition compared to the first edition concern only Chapters 5 and 6 and the Appendix A. Chapter 5 introduces the reader to the inverse problem of electrical impedance tomography.

This book highlights the latest developments on the numerical methods for inverse scattering problems associated with acoustic, electromagnetic, and elastic waves. Inverse scattering problems are concerned with identifying unknown or inaccessible objects by wave probing data, which makes possible many industrial and engineering applications including radar and sonar, medical imaging, nondestructive testing, remote sensing, and geophysical exploration. The mathematical study of inverse scattering problems is an active field of research. This book presents a comprehensive and unified mathematical treatment of various inverse scattering problems mainly from a numerical reconstruction perspective. It highlights the collaborative research outputs by the two groups of the authors yet surveys and reviews many existing results by global researchers in the literature. The book consists of three parts respectively corresponding to the studies on acoustic, electromagnetic, and elastic scattering problems. In each part, the authors start with in-depth theoretical and computational treatments of the forward scattering problems and then discuss various numerical reconstruction schemes for the associated inverse scattering problems in different scenarios of practical interest. In addition, the authors provide an overview of the existing results in the literature by other researchers. This book can serve as a handy reference for researchers or practitioners who are working on or implementing inverse scattering methods. It can also serve as a graduate textbook for research students who are interested in working on numerical algorithms for inverse scattering problems.

It has now been almost ten years since our first book on scattering theory ap peared [32]. At that time we claimed that "in recent years the development of integral equation methods for the direct scattering problem seems to be nearing completion, whereas the use of such an approach to study the inverse scattering problem has progressed to an extent that a 'state of the art' survey appears highly desirable". Since we wrote these words, the inverse scattering problem for acoustic and electromagnetic waves has grown from being a few theoreti cal considerations with limited numerical implementations to a weH developed mathematical theory with tested numerical algorithms. This maturing of the field of inverse scattering theory has been based on the realization that such problems are in general not only nonlinear but also improperly posed in the sense that the solution does not depend continuously on the measured data. This was emphasized in [32] and treated with the ideas and tools available at that time. Now, almost ten years later, these initial ideas have developed to the extent that a monograph summarizing the mathematical basis of the field seems appropriate. This book is oUf attempt to write such a monograph. The inverse scattering problem for acoustic and electromagnetic waves can broadly be divided into two classes, the inverse obstacle problem and the inverse medium problem.

Inverse problems are concerned with determining causes for observed or desired effects. Problems of this type appear in many application fields both in science and in engineering. The mathematical modelling of inverse problems usually leads to ill-posed problems, i.e., problems where solutions need not exist, need not be unique or may depend discontinuously on the data. For this reason, numerical methods for solving inverse problems are especially difficult, special methods have to be developed which are known under the term "regularization methods". This volume contains twelve survey papers about solution methods for inverse and ill-posed problems and about their application to specific types of inverse problems, e.g., in scattering theory, in tomography and medical applications, in geophysics and in image processing. The papers have been written by leading experts in the field and provide an up-to-date account of solution methods for inverse problems.

This classic book provides a rigorous treatment of the Riesz?Fredholm theory of compact operators in dual systems, followed by a derivation of the jump relations and mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations. Readers will benefit from a full discussion of the mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions, an in-depth treatment of the use of boundary integral equations to solve scattering problems for acoustic and electromagnetic waves, and an introduction to inverse scattering theory with an emphasis on the ill-posedness and nonlinearity of the inverse scattering problem.

Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.

Inverse problems in wave propagation occur in geophysics, ocean acoustics, civil and environmental engineering, ultrasonic non-destructive testing, biomedical ultrasonics, radar, astrophysics, as well as other areas of science and technology. The papers in this volume cover these scientific and technical topics, together with fundamental mathematical investigations of the relation between waves and scatterers.

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