Numerical Methods For Inverse Scattering Problems
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Numerical Methods For Inverse Scattering Problems
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Author : Jingzhi Li
language : en
Publisher: Springer Nature
Release Date : 2023-09-07
Numerical Methods For Inverse Scattering Problems written by Jingzhi Li and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-07 with Science categories.
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.
Inverse Problems In Partial Differential Equations
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Author : David L. Colton
language : en
Publisher: SIAM
Release Date : 1990-01-01
Inverse Problems In Partial Differential Equations written by David L. Colton and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.
Survey On Numerical Methods For Inverse Obstacle Scattering Problems
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Author : Xiaomao Deng
language : en
Publisher:
Release Date : 2010
Survey On Numerical Methods For Inverse Obstacle Scattering Problems written by Xiaomao Deng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Scattering (Mathematics) categories.
Surveys On Solution Methods For Inverse Problems
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Author : David Colton
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Surveys On Solution Methods For Inverse Problems written by David Colton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Ill Posed Problems In Natural Sciences
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Author : Andrei N. Tikhonov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-05-18
Ill Posed Problems In Natural Sciences written by Andrei N. Tikhonov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-18 with Mathematics categories.
No detailed description available for "Ill-Posed Problems in Natural Sciences".
The Linear Sampling Method In Inverse Electromagnetic Scattering
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Author : Fioralba Cakoni
language : en
Publisher: SIAM
Release Date : 2011-01-13
The Linear Sampling Method In Inverse Electromagnetic Scattering written by Fioralba Cakoni and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-13 with Mathematics categories.
A complete description of the linear sampling method for electromagnetic waves, important for those researching inverse electromagnetic scattering theory.
Mathematical Methods In Tomography
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Author : Gabor T. Herman
language : en
Publisher: Springer
Release Date : 2006-11-14
Mathematical Methods In Tomography written by Gabor T. Herman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Medical categories.
The conference was devoted to the discussion of present and future techniques in medical imaging, including 3D x-ray CT, ultrasound and diffraction tomography, and biomagnetic ima- ging. The mathematical models, their theoretical aspects and the development of algorithms were treated. The proceedings contains surveys on reconstruction in inverse obstacle scat- tering, inversion in 3D, and constrained least squares pro- blems.Research papers include besides the mentioned imaging techniques presentations on image reconstruction in Hilbert spaces, singular value decompositions, 3D cone beam recon- struction, diffuse tomography, regularization of ill-posed problems, evaluation reconstruction algorithms and applica- tions in non-medical fields. Contents: Theoretical Aspects: J.Boman: Helgason' s support theorem for Radon transforms-a newproof and a generalization -P.Maass: Singular value de- compositions for Radon transforms- W.R.Madych: Image recon- struction in Hilbert space -R.G.Mukhometov: A problem of in- tegral geometry for a family of rays with multiple reflec- tions -V.P.Palamodov: Inversion formulas for the three-di- mensional ray transform - Medical Imaging Techniques: V.Friedrich: Backscattered Photons - are they useful for a surface - near tomography - P.Grangeat: Mathematical frame- work of cone beam 3D reconstruction via the first derivative of the Radon transform -P.Grassin,B.Duchene,W.Tabbara: Dif- fraction tomography: some applications and extension to 3D ultrasound imaging -F.A.Gr}nbaum: Diffuse tomography: a re- fined model -R.Kress,A.Zinn: Three dimensional reconstruc- tions in inverse obstacle scattering -A.K.Louis: Mathemati- cal questions of a biomagnetic imaging problem - Inverse Problems and Optimization: Y.Censor: On variable block algebraic reconstruction techniques -P.P.Eggermont: On Volterra-Lotka differential equations and multiplicative algorithms for monotone complementary problems
Iterative Methods For Approximate Solution Of Inverse Problems
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Author : A.B. Bakushinsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-02-15
Iterative Methods For Approximate Solution Of Inverse Problems written by A.B. Bakushinsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-15 with Mathematics categories.
This volume presents a unified approach to constructing iterative methods for solving irregular operator equations and provides rigorous theoretical analysis for several classes of these methods. The analysis of methods includes convergence theorems as well as necessary and sufficient conditions for their convergence at a given rate. The principal groups of methods studied in the book are iterative processes based on the technique of universal linear approximations, stable gradient-type processes, and methods of stable continuous approximations. Compared to existing monographs and textbooks on ill-posed problems, the main distinguishing feature of the presented approach is that it doesn’t require any structural conditions on equations under consideration, except for standard smoothness conditions. This allows to obtain in a uniform style stable iterative methods applicable to wide classes of nonlinear inverse problems. Practical efficiency of suggested algorithms is illustrated in application to inverse problems of potential theory and acoustic scattering. The volume can be read by anyone with a basic knowledge of functional analysis. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems.
Numerical Comparison Of Some Reconstruction Methods For Inverse Scattering Problems
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Author : Keji Liu
language : en
Publisher:
Release Date : 2011
Numerical Comparison Of Some Reconstruction Methods For Inverse Scattering Problems written by Keji Liu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Inverse problems (Differential equations) categories.
An Introduction To Inverse Scattering And Inverse Spectral Problems
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Author : Khosrow Chadan
language : en
Publisher: SIAM
Release Date : 1997-01-01
An Introduction To Inverse Scattering And Inverse Spectral Problems written by Khosrow Chadan and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Mathematics categories.
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.