Numerical Methods For Inverse Scattering Problems

Author : Jingzhi Li,Hongyu Liu
Publisher : Springer Nature
Page : 373 pages
File Size : 53,7 Mb
Release : 2023-09-07
Category : Science
ISBN : 9789819937721

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Numerical Methods for Inverse Scattering Problems by Jingzhi Li,Hongyu Liu Pdf

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.

Author : David Colton,Heinz W. Engl,Alfred K. Louis,Joyce McLaughlin,William Rundell
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783709162965

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Surveys on Solution Methods for Inverse Problems by David Colton,Heinz W. Engl,Alfred K. Louis,Joyce McLaughlin,William Rundell Pdf

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.

Author : David H. Sattinger
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 41,6 Mb
Release : 1991
Category : Mathematics
ISBN : 9780821851296

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Inverse Scattering and Applications by David H. Sattinger Pdf

This book presents papers given at a Conference on Inverse Scattering on the Line, held in June 1990 at the University of Massachusetts, Amherst. A wide variety of topics in inverse problems were covered: inverse scattering problems on the line; inverse problems in higher dimensions; inverse conductivity problems; and numerical methods. In addition, problems from statistical physics were covered, including monodromy problems, quantum inverse scattering, and the Bethe ansatz. One of the aims of the conference was to bring together researchers in a variety of areas of inverse problems which have seen intensive activity in recent years. scattering

Author : David Colton,Rainer Kress
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 53,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662028353

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Inverse Acoustic and Electromagnetic Scattering Theory by David Colton,Rainer Kress Pdf

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.

Author : Khosrow Chadan,David Colton,William Rundell,Lassi P?iv?rinta
Publisher : SIAM
Page : 208 pages
File Size : 53,7 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 0898719712

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An Introduction to Inverse Scattering and Inverse Spectral Problems by Khosrow Chadan,David Colton,William Rundell,Lassi P?iv?rinta Pdf

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.

Author : David Colton,Rainer Kress
Publisher : Springer Nature
Page : 518 pages
File Size : 46,9 Mb
Release : 2019-11-06
Category : Mathematics
ISBN : 9783030303518

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Inverse Acoustic and Electromagnetic Scattering Theory by David Colton,Rainer Kress Pdf

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.

Author : Alexander G. Ramm
Publisher : Unknown
Page : 34 pages
File Size : 40,8 Mb
Release : 1987
Category : Electronic
ISBN : CORNELL:31924074851928

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Numerical Method for Solving 3d Inverse Scattering Problem by Alexander G. Ramm Pdf

Author : Alexander G. Ramm
Publisher : Springer Nature
Page : 53 pages
File Size : 46,8 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 9783031024184

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Inverse Obstacle Scattering with Non-Over-Determined Scattering Data by Alexander G. Ramm Pdf

The inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering (;;), where (;;) is the scattering amplitude, ; 2 is the direction of the scattered, incident wave, respectively, 2 is the unit sphere in the R3 and k > 0 is the modulus of the wave vector. The scattering data is called non-over-determined if its dimensionality is the same as the one of the unknown object. By the dimensionality one understands the minimal number of variables of a function describing the data or an object. In an inverse obstacle scattering problem this number is 2, and an example of non-over-determined data is () := (;0;0). By sub-index 0 a fixed value of a variable is denoted. It is proved in this book that the data (), known for all in an open subset of 2, determines uniquely the surface and the boundary condition on . This condition can be the Dirichlet, or the Neumann, or the impedance type. The above uniqueness theorem is of principal importance because the non-over-determined data are the minimal data determining uniquely the unknown . There were no such results in the literature, therefore the need for this book arose. This book contains a self-contained proof of the existence and uniqueness of the scattering solution for rough surfaces.

Author : Fioralba Cakoni,David Colton,Peter Monk
Publisher : SIAM
Page : 147 pages
File Size : 47,7 Mb
Release : 2011-01-01
Category : Mathematics
ISBN : 9780898719406

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The Linear Sampling Method in Inverse Electromagnetic Scattering by Fioralba Cakoni,David Colton,Peter Monk Pdf

The linear sampling method is the oldest and most developed of the qualitative methods in inverse scattering theory. It is based on solving a linear integral equation and then using the equation's solution as an indicator function for the determination of the support of the scattering object. This book describes the linear sampling method for a variety of electromagnetic scattering problems. It presents uniqueness theorems and the derivation of various inequalities on the material properties of the scattering object from a knowledge of the far field pattern of the scattered wave.

Author : Dinh-Liem Nguyen,Loc Hoang Nguyen,Thi-Phong Nguyen
Publisher : American Mathematical Society
Page : 218 pages
File Size : 42,7 Mb
Release : 2023-04-12
Category : Mathematics
ISBN : 9781470469689

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Advances in Inverse Problems for Partial Differential Equations by Dinh-Liem Nguyen,Loc Hoang Nguyen,Thi-Phong Nguyen Pdf

This volume contains the proceedings of two AMS Special Sessions “Recent Developments on Analysis and Computation for Inverse Problems for PDEs,” virtually held on March 13–14, 2021, and “Recent Advances in Inverse Problems for Partial Differential Equations,” virtually held on October 23–24, 2021. The papers in this volume focus on new results on numerical methods for various inverse problems arising in electrical impedance tomography, inverse scattering in radar and optics problems, reconstruction of initial conditions, control of acoustic fields, and stock price forecasting. The authors studied iterative and non-iterative approaches such as optimization-based, globally convergent, sampling, and machine learning-based methods. The volume provides an interesting source on advances in computational inverse problems for partial differential equations.

Author : Pierre C. Sabatier
Publisher : Springer Science & Business Media
Page : 645 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642752988

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Inverse Methods in Action by Pierre C. Sabatier Pdf

This volume contains the Proceedings of a meeting held at Montpellier from November 27th to December 1st 1989 and entitled "Inverse Problems Multicen tennials Meeting". It was held in honor of two major centennials: the foundation of Montpellier University in 1289 and the French Revolution of 1789. The meet ing was one of a series of annual meetings on interdisciplinary aspects of inverse problems organized in Montpellier since 1972 and known as "RCP 264". The meeting was sponsored by the Centre National de la Recherche Scientifique (con tract GR 264) and by the Direction des Recherches et Etudes Techniques (contract 88 CO 283). The Proceedings are presented by chapters on different topics, the choice of topic often being arbitrary. The chapter titles are "Tomographic Inverse Problems", "Distributed Parameters Inverse Problems", "Spectral Inverse Problems (Exact Methods)", "Theoretical hnaging", "Wave Propagation and Scattering Problems (hnaging and Numerical Methods)", "Miscellaneous Problems", "Inverse Methods and Applications to Nonlinear Problems". In each chapter but the first, the papers have been sorted alphabetically according to author*. In the first chapter, a set of theoretical papers is presented first, then more applied ones. There are so many well-known and excellent lectures that I will not try to refer to them all here (the reader will be easily convinced by reading the Table of Contents). My comments at the conference are summarized by the short scientific introduction at the beginning of the volume.

Author : David L. Colton,Richard E. Ewing,William Rundell,Society for Industrial and Applied Mathematics
Publisher : SIAM
Page : 234 pages
File Size : 48,8 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 0898712521

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Inverse Problems in Partial Differential Equations by David L. Colton,Richard E. Ewing,William Rundell,Society for Industrial and Applied Mathematics Pdf

Author : Alexander G. Ramm
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 55,9 Mb
Release : 2005-12-19
Category : Technology & Engineering
ISBN : 9780387232188

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Inverse Problems by Alexander G. Ramm Pdf

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.

Author : Pierre Célestin Sabatier
Publisher : Unknown
Page : 600 pages
File Size : 50,7 Mb
Release : 1987
Category : Mathematics
ISBN : UVA:X001324042

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Inverse Problems by Pierre Célestin Sabatier Pdf

Author : Xudong Chen
Publisher : John Wiley & Sons
Page : 328 pages
File Size : 51,5 Mb
Release : 2018-03-07
Category : Science
ISBN : 9781119312017

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Computational Methods for Electromagnetic Inverse Scattering by Xudong Chen Pdf

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