A qualitative approach to inverse scattering theory
 Responsibility
 Fioralba Cakoni, David Colton.
 Language
 English.
 Publication
 New York : Springer, [2014]
 Physical description
 x, 297 pages : illustrations ; 25 cm.
 Series
 Applied mathematical sciences (SpringerVerlag New York Inc.) ; v. 188.
Access
Available online
Math & Statistics Library
Stacks
Call number  Status 

QC20.7 .S3 C37 2014  Unknown 
More options
Creators/Contributors
 Author/Creator
 Cakoni, Fioralba, author.
 Contributor
 Colton, David L., 1943 author.
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 287294) and index.
 Contents

 Functional analysis and Sobolev spaces
 Normed spaces
 Bounded linear operators
 Adjoint operator
 Sobolev space Hp (...)
 Sobolev space Hp (dD)
 Illposed problems
 Regularization methods
 Singular value decomposition
 Tikhonov regularization
 Scattering by imperfect conductors
 Maxwell's equations
 Bessel functions
 Direct scattering problem
 Inverse scattering problems for imperfect conductors
 Farfield patterns
 Uniqueness theorems for inverse problem
 Linear sampling method
 Determination of surface impedance
 Limited aperture data
 Nearfield data
 Scattering by orthotropic media
 Maxwell equations for an orthotropic medium
 Mathematical formulation of direct scattering problem
 Variational methods
 Solution of direct scattering problem
 Inverse scattering problems for orthotropic media
 Formulation of inverse problem
 Interior transmission problem
 Transmission eigenvahle problern
 The case n = 1
 The case n ... 1
 Discreteness of transmission eigenvalues
 Existence of transmission eigenvalues for n ... 1
 Uniqueness
 Linear sampling method
 Determination of transmission eigenvalues from farfield data
 Factorization methods
 Factorization method for obstacle scattering
 Preliminary results
 Properties of farfield operator
 Factorization method
 Factorization method for an inhomogeneous medium
 Preliminary results
 Properties of farfield operator
 Factorization method
 Justification of linear sampling method
 Closing remarks
 Mixed boundary value problems
 Scattering by a partially coated perfect conductor
 Inverse scattering problem for partially coated perfect conductor
 Numerical examples
 Scattering by partially coated dielectric
 Inverse scattering problem for partially coated dielectric
 Numerical examples
 Scattering by cracks
 Inverse scattering problem for cracks
 Numerical examples
 Inverse spectral problems for transmission eigenvalues
 Entire functions
 Transformation operators
 Transmission eigenvalues
 An inverse spectral theorem
 A glimpse at maxwell's equations
 References
 Index.
 Publisher's Summary
 Inverse scattering theory is an important area of applied mathematics due to its central role in such areas as medical imaging , nondestructive testing and geophysical exploration. Until recently all existing algorithms for solving inverse scattering problems were based on using either a weak scattering assumption or on the use of nonlinear optimization techniques. The limitations of these methods have led in recent years to an alternative approach to the inverse scattering problem which avoids the incorrect model assumptions inherent in the use of weak scattering approximations as well as the strong a priori information needed in order to implement nonlinear optimization techniques. These new methods come under the general title of qualitative methods in inverse scattering theory and seek to determine an approximation to the shape of the scattering object as well as estimates on its material properties without making any weak scattering assumption and using essentially no a priori information on the nature of the scattering object. This book is designed to be an introduction to this new approach in inverse scattering theory focusing on the use of sampling methods and transmission eigenvalues. In order to aid the reader coming from a discipline outside of mathematics we have included background material on functional analysis, Sobolev spaces, the theory of ill posed problems and certain topics in in the theory of entire functions of a complex variable. This book is an updated and expanded version of an earlier book by the authors published by Springer titled Qualitative Methods in Inverse Scattering Theory Review of Qualitative Methods in Inverse Scattering Theory All in all, the authors do exceptionally well in combining such a wide variety of mathematical material and in presenting it in a wellorganized and easytofollow fashion. This text certainly complements the growing body of work in inverse scattering and should well suit both new researchers to the field as well as those who could benefit from such a nice codified collection of profitable results combined in one bound volume. SIAM Review, 2006.
(source: Nielsen Book Data)  Included Work
 Cakoni, Fioralba. Qualitative methods in inverse scattering theory, author.
Subjects
Bibliographic information
 Publication date
 2014
 Series
 Applied mathematical sciences, 00665452 ; Volume 188
 Note
 Previously published as: Qualitative methods in inverse scattering theory.
 Available in another form
 ( 9781461488279 (online) )
 Available in another form
 ISBN
 9781461488262 (hd.bd.)
 9781461488279 (online)
 1461488265 (hd.bd.)
 1461488273 (eBook)