Inverse Problem Theory
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Inverse Problem Theory And Methods For Model Parameter Estimation
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Author : Albert Tarantola
language : en
Publisher: SIAM
Release Date : 2005-01-01
Inverse Problem Theory And Methods For Model Parameter Estimation written by Albert Tarantola and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
While the prediction of observations is a forward problem, the use of actual observations to infer the properties of a model is an inverse problem. Inverse problems are difficult because they may not have a unique solution. The description of uncertainties plays a central role in the theory, which is based on probability theory. This book proposes a general approach that is valid for linear as well as for nonlinear problems. The philosophy is essentially probabilistic and allows the reader to understand the basic difficulties appearing in the resolution of inverse problems. The book attempts to explain how a method of acquisition of information can be applied to actual real-world problems, and many of the arguments are heuristic.
An Introduction To The Mathematical Theory Of Inverse Problems
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Author : Andreas Kirsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-24
An Introduction To The Mathematical Theory Of Inverse Problems written by Andreas Kirsch 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 2011-03-24 with Mathematics categories.
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.
Inverse Problem Theory And Methods For Model Parameter Estimation
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Author : Albert Tarantola
language : en
Publisher: SIAM
Release Date : 2005-01-01
Inverse Problem Theory And Methods For Model Parameter Estimation written by Albert Tarantola and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
This book proposes a general approach to the basic difficulties appearing in the resolution of inverse problems.
Computational Methods For Inverse Problems
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Author : Curtis R. Vogel
language : en
Publisher: SIAM
Release Date : 2002-01-01
Computational Methods For Inverse Problems written by Curtis R. Vogel and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
Geophysical Data Analysis
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Author : William Menke
language : en
Publisher: Elsevier
Release Date : 1989-10-04
Geophysical Data Analysis written by William Menke and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-10-04 with Science categories.
Please use extracts from reviews of first editionKey Features* Updated and thoroughly revised edition* additional material on geophysical/acoustic tomography* Detailed discussion of application of inverse theory to tectonic, gravitational and geomagnetic studies
Parameter Estimation And Inverse Problems
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Author : Richard C. Aster
language : en
Publisher: Elsevier
Release Date : 2018-10-16
Parameter Estimation And Inverse Problems written by Richard C. Aster and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-16 with Science categories.
Parameter Estimation and Inverse Problems, Third Edition, is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who do not have an extensive mathematical background. The book is complemented by a companion website that includes MATLAB codes that correspond to examples that are illustrated with simple, easy to follow problems that illuminate the details of particular numerical methods. Updates to the new edition include more discussions of Laplacian smoothing, an expansion of basis function exercises, the addition of stochastic descent, an improved presentation of Fourier methods and exercises, and more. - Features examples that are illustrated with simple, easy to follow problems that illuminate the details of a particular numerical method - Includes an online instructor's guide that helps professors teach and customize exercises and select homework problems - Covers updated information on adjoint methods that are presented in an accessible manner
Inverse And Ill Posed Problems
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Author : Sergey I. Kabanikhin
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-23
Inverse And Ill Posed Problems written by Sergey I. Kabanikhin and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-23 with Mathematics categories.
The theory of ill-posed problems originated in an unusual way. As a rule, a new concept is a subject in which its creator takes a keen interest. The concept of ill-posed problems was introduced by Hadamard with the comment that these problems are physically meaningless and not worthy of the attention of serious researchers. Despite Hadamard's pessimistic forecasts, however, his unloved "child" has turned into a powerful theory whose results are used in many fields of pure and applied mathematics. What is the secret of its success? The answer is clear. Ill-posed problems occur everywhere and it is unreasonable to ignore them. Unlike ill-posed problems, inverse problems have no strict mathematical definition. In general, they can be described as the task of recovering a part of the data of a corresponding direct (well-posed) problem from information about its solution. Inverse problems were first encountered in practice and are mostly ill-posed. The urgent need for their solution, especially in geological exploration and medical diagnostics, has given powerful impetus to the development of the theory of ill-posed problems. Nowadays, the terms "inverse problem" and "ill-posed problem" are inextricably linked to each other. Inverse and ill-posed problems are currently attracting great interest. A vast literature is devoted to these problems, making it necessary to systematize the accumulated material. This book is the first small step in that direction. We propose a classification of inverse problems according to the type of equation, unknowns and additional information. We consider specific problems from a single position and indicate relationships between them. The problems relate to different areas of mathematics, such as linear algebra, theory of integral equations, integral geometry, spectral theory and mathematical physics. We give examples of applied problems that can be studied using the techniques we describe. This book was conceived as a textbook on the foundations of the theory of inverse and ill-posed problems for university students. The author's intention was to explain this complex material in the most accessible way possible. The monograph is aimed primarily at those who are just beginning to get to grips with inverse and ill-posed problems but we hope that it will be useful to anyone who is interested in the subject.
An Introduction To Data Analysis And Uncertainty Quantification For Inverse Problems
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Author : Luis Tenorio
language : en
Publisher: SIAM
Release Date : 2017-07-06
An Introduction To Data Analysis And Uncertainty Quantification For Inverse Problems written by Luis Tenorio and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-06 with Mathematics categories.
Inverse problems are found in many applications, such as medical imaging, engineering, astronomy, and geophysics, among others. To solve an inverse problem is to recover an object from noisy, usually indirect observations. Solutions to inverse problems are subject to many potential sources of error introduced by approximate mathematical models, regularization methods, numerical approximations for efficient computations, noisy data, and limitations in the number of observations; thus it is important to include an assessment of the uncertainties as part of the solution. Such assessment is interdisciplinary by nature, as it requires, in addition to knowledge of the particular application, methods from applied mathematics, probability, and statistics. This book bridges applied mathematics and statistics by providing a basic introduction to probability and statistics for uncertainty quantification in the context of inverse problems, as well as an introduction to statistical regularization of inverse problems. The author covers basic statistical inference, introduces the framework of ill-posed inverse problems, and explains statistical questions that arise in their applications. An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems?includes many examples that explain techniques which are useful to address general problems arising in uncertainty quantification, Bayesian and non-Bayesian statistical methods and discussions of their complementary roles, and analysis of a real data set to illustrate the methodology covered throughout the book.
Mathematical Modelling
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Author : Seppo Pohjolainen
language : en
Publisher: Springer
Release Date : 2016-07-14
Mathematical Modelling written by Seppo Pohjolainen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-14 with Mathematics categories.
This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.
The Inverse Problem Of Scattering Theory
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Author : Z.S. Agranovich
language : en
Publisher: Courier Dover Publications
Release Date : 2020-05-21
The Inverse Problem Of Scattering Theory written by Z.S. Agranovich and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-21 with Mathematics categories.
This monograph by two Soviet experts in mathematical physics was a major contribution to inverse scattering theory. The two-part treatment examines the boundary-value problem with and without singularities. 1963 edition.