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Author | : Fioralba Cakoni |
Publisher | : SIAM |
Total Pages | : 147 |
Release | : 2011-01-01 |
Genre | : Mathematics |
ISBN | : 0898719402 |
Download The Linear Sampling Method in Inverse Electromagnetic Scattering Book in PDF, ePub and Kindle
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 | : David Colton |
Publisher | : Springer Nature |
Total Pages | : 518 |
Release | : 2019-11-06 |
Genre | : Mathematics |
ISBN | : 3030303519 |
Download Inverse Acoustic and Electromagnetic Scattering Theory Book in PDF, ePub and Kindle
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 | : Fioralba Cakoni |
Publisher | : Springer Science & Business Media |
Total Pages | : 232 |
Release | : 2005-12-29 |
Genre | : Mathematics |
ISBN | : 3540312307 |
Download Qualitative Methods in Inverse Scattering Theory Book in PDF, ePub and Kindle
Inverse scattering theory has been a particularly active and successful field in applied mathematics and engineering for the past twenty years. The increasing demands of imaging and target identification require new powerful and flexible techniques besides the existing weak scattering approximation or nonlinear optimization methods. One class of such methods comes under the general description of qualitative methods in inverse scattering theory. This textbook is an easily-accessible "class-tested" introduction to the field. It is accessible also to readers who are not professional mathematicians, thus making these new mathematical ideas in inverse scattering theory available to the wider scientific and engineering community.
Author | : David Colton |
Publisher | : Springer Science & Business Media |
Total Pages | : 316 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662028352 |
Download Inverse Acoustic and Electromagnetic Scattering Theory Book in PDF, ePub and Kindle
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 | : |
Publisher | : |
Total Pages | : |
Release | : 2017 |
Genre | : |
ISBN | : |
Download DIRECT SAMPLING METHODS FOR INVERSE SCATTERING PROBLEMS Book in PDF, ePub and Kindle
Abstract : Recently, direct sampling methods became popular for solving inverse scattering problems to estimate the shape of the scattering object. They provide a simple tool to directly reconstruct the shape of the unknown scatterer. These methods are based on choosing an appropriate indicator function f on Rd, d=2 or 3, such that f(z) decides whether z lies inside or outside the scatterer. Consequently, we can determine the location and the shape of the unknown scatterer. In this thesis, we first present some sampling methods for shape reconstruction in inverse scattering problems. These methods, which are described in Chapter 1, include Multiple Signal Classification (MUSIC) by Devaney, the Linear Sampling Method (LSM) by Colton and Kirsch, the Factorization Method by Kirsch, and the Direct Sampling Method by Ito et al. In Chapter 2, we introduce some direct sampling methods, including Orthogonality Sampling by Potthast and a direct sampling method using far field measurements for shape reconstruction by Liu. In Chapter 3, we generalize Liu's method for shape reconstruction in inverse electromagnetic scattering problems. The method applies in an inhomogeneous isotropic medium in R3 and uses the far field measurements. We study the behavior of the new indicator for the sampling points both outside and inside the scatterer. In Chapter 4, we propose a new sampling method for multifrequency inverse source problem for time-harmonic acoustics using a finite set of far field data. We study the theoretical foundation of the proposed sampling method, and present some numerical experiments to demonstrate the feasibility and effectiveness of the method. Final conclusions of this thesis are summarized in Chapter 5. Recommendations for possible future works are also given in this chapter.
Author | : Xudong Chen |
Publisher | : John Wiley & Sons |
Total Pages | : 325 |
Release | : 2018-07-18 |
Genre | : Science |
ISBN | : 1119311985 |
Download Computational Methods for Electromagnetic Inverse Scattering Book in PDF, ePub and Kindle
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
Author | : Jingzhi Li |
Publisher | : Springer Nature |
Total Pages | : 373 |
Release | : 2023-09-07 |
Genre | : Science |
ISBN | : 9819937728 |
Download Numerical Methods for Inverse Scattering Problems Book in PDF, ePub and Kindle
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 L. Colton |
Publisher | : |
Total Pages | : 24 |
Release | : 1999 |
Genre | : |
ISBN | : |
Download The Linear Sampling Method in Inverse Scattering Theory Book in PDF, ePub and Kindle
Author | : Roland Potthast |
Publisher | : CRC Press |
Total Pages | : 277 |
Release | : 2001-05-30 |
Genre | : Mathematics |
ISBN | : 1420035487 |
Download Point Sources and Multipoles in Inverse Scattering Theory Book in PDF, ePub and Kindle
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
Author | : Khosrow Chadan |
Publisher | : SIAM |
Total Pages | : 206 |
Release | : 1997-01-01 |
Genre | : Mathematics |
ISBN | : 0898713870 |
Download An Introduction to Inverse Scattering and Inverse Spectral Problems Book in PDF, ePub and Kindle
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.