An Introduction To The Mathematical Theory Of Inverse Problems

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An Introduction to the Mathematical Theory of Inverse Problems

Andreas Kirsch
An Introduction to the Mathematical Theory of Inverse Problems Book PDF

Author : Andreas Kirsch
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 55,6 Mb
Release : 2011-03-24
Category : Mathematics
ISBN : 9781441984746

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An Introduction to the Mathematical Theory of Inverse Problems by Andreas Kirsch Pdf

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.

An Introduction to the Mathematical Theory of Inverse Problems

Andreas Kirsch
An Introduction to the Mathematical Theory of Inverse Problems Book PDF

Author : Andreas Kirsch
Publisher : Springer
Page : 0 pages
File Size : 54,9 Mb
Release : 2012-08-14
Category : Science
ISBN : 1461253381

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An Introduction to the Mathematical Theory of Inverse Problems by Andreas Kirsch Pdf

Following Keller [119] we call two problems inverse to each other if the for mulation of each of them requires full or partial knowledge of the other. By this definition, it is obviously arbitrary which of the two problems we call the direct and which we call the inverse problem. But usually, one of the problems has been studied earlier and, perhaps, in more detail. This one is usually called the direct problem, whereas the other is the inverse problem. However, there is often another, more important difference between these two problems. Hadamard (see [91]) introduced the concept of a well-posed problem, originating from the philosophy that the mathematical model of a physical problem has to have the properties of uniqueness, existence, and stability of the solution. If one of the properties fails to hold, he called the problem ill-posed. It turns out that many interesting and important inverse in science lead to ill-posed problems, while the corresponding di problems rect problems are well-posed. Often, existence and uniqueness can be forced by enlarging or reducing the solution space (the space of "models"). For restoring stability, however, one has to change the topology of the spaces, which is in many cases impossible because of the presence of measurement errors. At first glance, it seems to be impossible to compute the solution of a problem numerically if the solution of the problem does not depend continuously on the data, i. e. , for the case of ill-posed problems.

Inverse Problems

Mathias Richter
Inverse Problems Book PDF

Author : Mathias Richter
Publisher : Springer Nature
Page : 281 pages
File Size : 54,7 Mb
Release : 2021-01-05
Category : Mathematics
ISBN : 9783030593179

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Inverse Problems by Mathias Richter Pdf

This textbook is an introduction to the subject of inverse problems with an emphasis on practical solution methods and applications from geophysics. The treatment is mathematically rigorous, relying on calculus and linear algebra only; familiarity with more advanced mathematical theories like functional analysis is not required. Containing up-to-date methods, this book will provide readers with the tools necessary to compute regularized solutions of inverse problems. A variety of practical examples from geophysics are used to motivate the presentation of abstract mathematical ideas, thus assuring an accessible approach. Beginning with four examples of inverse problems, the opening chapter establishes core concepts, such as formalizing these problems as equations in vector spaces and addressing the key issue of ill-posedness. Chapter Two then moves on to the discretization of inverse problems, which is a prerequisite for solving them on computers. Readers will be well-prepared for the final chapters that present regularized solutions of inverse problems in finite-dimensional spaces, with Chapter Three covering linear problems and Chapter Four studying nonlinear problems. Model problems reflecting scenarios of practical interest in the geosciences, such as inverse gravimetry and full waveform inversion, are fully worked out throughout the book. They are used as test cases to illustrate all single steps of solving inverse problems, up to numerical computations. Five appendices include the mathematical foundations needed to fully understand the material. This second edition expands upon the first, particularly regarding its up-to-date treatment of nonlinear problems. Following the author’s approach, readers will understand the relevant theory and methodology needed to pursue more complex applications. Inverse Problems is ideal for graduate students and researchers interested in geophysics and geosciences.

Inverse Problems in the Mathematical Sciences

Charles W. Groetsch
Inverse Problems in the Mathematical Sciences Book PDF

Author : Charles W. Groetsch
Publisher : Springer Science & Business Media
Page : 154 pages
File Size : 53,8 Mb
Release : 2013-12-14
Category : Technology & Engineering
ISBN : 9783322992024

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Inverse Problems in the Mathematical Sciences by Charles W. Groetsch Pdf

Inverse problems are immensely important in modern science and technology. However, the broad mathematical issues raised by inverse problems receive scant attention in the university curriculum. This book aims to remedy this state of affairs by supplying an accessible introduction, at a modest mathematical level, to the alluring field of inverse problems. Many models of inverse problems from science and engineering are dealt with and nearly a hundred exercises, of varying difficulty, involving mathematical analysis, numerical treatment, or modelling of inverse problems, are provided. The main themes of the book are: causation problem modeled as integral equations; model identification problems, posed as coefficient determination problems in differential equations; the functional analytic framework for inverse problems; and a survey of the principal numerical methods for inverse problems. An extensive annotated bibliography furnishes leads on the history of inverse problems and a guide to the frontiers of current research.

Inside Out

Gunther Uhlmann
Inside Out Book PDF

Author : Gunther Uhlmann
Publisher : Cambridge University Press
Page : 424 pages
File Size : 48,7 Mb
Release : 2003-11-10
Category : Mathematics
ISBN : 0521824699

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Inside Out by Gunther Uhlmann Pdf

In this book, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics.

Methods for Solving Inverse Problems in Mathematical Physics

Global Express Ltd. Co.,Aleksey I. Prilepko,Dmitry G. Orlovsky,Igor A. Vasin
Methods for Solving Inverse Problems in Mathematical Physics Book PDF

Author : Global Express Ltd. Co.,Aleksey I. Prilepko,Dmitry G. Orlovsky,Igor A. Vasin
Publisher : CRC Press
Page : 736 pages
File Size : 50,9 Mb
Release : 2000-03-21
Category : Mathematics
ISBN : 0824719875

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Methods for Solving Inverse Problems in Mathematical Physics by Global Express Ltd. Co.,Aleksey I. Prilepko,Dmitry G. Orlovsky,Igor A. Vasin Pdf

Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for all principal types of partial differential equations. It covers up-to-date methods of linear and nonlinear analysis, the theory of differential equations in Banach spaces, applications of functional analysis, and semigroup theory.

Parameter Estimation and Inverse Problems

Richard C. Aster,Brian Borchers,Clifford H. Thurber
Parameter Estimation and Inverse Problems Book PDF

Author : Richard C. Aster,Brian Borchers,Clifford H. Thurber
Publisher : Elsevier
Page : 404 pages
File Size : 48,6 Mb
Release : 2018-10-16
Category : Science
ISBN : 9780128134238

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Parameter Estimation and Inverse Problems by Richard C. Aster,Brian Borchers,Clifford H. Thurber Pdf

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

Computational Methods for Inverse Problems

Curtis R. Vogel
Computational Methods for Inverse Problems Book PDF

Author : Curtis R. Vogel
Publisher : SIAM
Page : 195 pages
File Size : 52,8 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 9780898717570

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Computational Methods for Inverse Problems by Curtis R. Vogel Pdf

Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.

Introduction to Inverse Problems in Imaging

M. Bertero,P. Boccacci
Introduction to Inverse Problems in Imaging Book PDF

Author : M. Bertero,P. Boccacci
Publisher : CRC Press
Page : 366 pages
File Size : 47,5 Mb
Release : 2020-08-30
Category : Technology & Engineering
ISBN : 1439822069

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Introduction to Inverse Problems in Imaging by M. Bertero,P. Boccacci Pdf

This is a graduate textbook on the principles of linear inverse problems, methods of their approximate solution, and practical application in imaging. The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of readers from different backgrounds in science and engineering. Mathematical prerequisites are first courses in analysis, geometry, linear algebra, probability theory, and Fourier analysis. The authors concentrate on presenting easily implementable and fast solution algorithms. With examples and exercises throughout, the book will provide the reader with the appropriate background for a clear understanding of the essence of inverse problems (ill-posedness and its cure) and, consequently, for an intelligent assessment of the rapidly growing literature on these problems.

An Introduction to Inverse Scattering and Inverse Spectral Problems

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

Author : Khosrow Chadan,David Colton,William Rundell,Lassi P?iv?rinta
Publisher : SIAM
Page : 208 pages
File Size : 55,7 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.

Handbook of Mathematical Methods in Imaging

Otmar Scherzer
Handbook of Mathematical Methods in Imaging Book PDF

Author : Otmar Scherzer
Publisher : Springer Science & Business Media
Page : 1626 pages
File Size : 43,9 Mb
Release : 2010-11-23
Category : Mathematics
ISBN : 9780387929194

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Handbook of Mathematical Methods in Imaging by Otmar Scherzer Pdf

The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Inverse Problems

Kazufumi Ito,Bangti Jin
Inverse Problems Book PDF

Author : Kazufumi Ito,Bangti Jin
Publisher : World Scientific Publishing Company Incorporated
Page : 319 pages
File Size : 46,9 Mb
Release : 2014-07
Category : Mathematics
ISBN : 9814596191

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Inverse Problems by Kazufumi Ito,Bangti Jin Pdf

Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a valuable contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are discussed in detail. The mathematical theory focuses on nonsmooth Tikhonov regularization for linear and nonlinear inverse problems. The computational methods include nonsmooth optimization algorithms, direct inversion methods and uncertainty quantification via Bayesian inference. The book offers a comprehensive treatment of modern techniques, and seamlessly blends regularization theory with computational methods, which is essential for developing accurate and efficient inversion algorithms for many practical inverse problems. It demonstrates many current developments in the field of computational inversion, such as value function calculus, augmented Tikhonov regularization, multi-parameter Tikhonov regularization, semismooth Newton method, direct sampling method, uncertainty quantification and approximate Bayesian inference. It is written for graduate students and researchers in mathematics, natural science and engineering.

逆问题数学理论导论/An Introduction to the Mathematical Theory of Inverse Problems/Grauate Texts in Mathematics

Andreas Kirsch,基尔希
An Introduction to the Mathematical Theory of Inverse Problems Grauate Texts in Mathematics Book PDF

Author : Andreas Kirsch,基尔希
Publisher : Unknown
Page : 282 pages
File Size : 53,8 Mb
Release : 1996
Category : Inverse problems (Differential equations)
ISBN : 7506242516

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逆问题数学理论导论/An Introduction to the Mathematical Theory of Inverse Problems/Grauate Texts in Mathematics by Andreas Kirsch,基尔希 Pdf

本书英文题名来自于书名页

Inverse Problem Theory and Methods for Model Parameter Estimation

Albert Tarantola
Inverse Problem Theory and Methods for Model Parameter Estimation Book PDF

Author : Albert Tarantola
Publisher : SIAM
Page : 349 pages
File Size : 51,8 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 0898717922

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Inverse Problem Theory and Methods for Model Parameter Estimation by Albert Tarantola Pdf

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.

Discrete Inverse Problems

Per Christian Hansen
Discrete Inverse Problems Book PDF

Author : Per Christian Hansen
Publisher : SIAM
Page : 220 pages
File Size : 54,7 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9780898718836

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Discrete Inverse Problems by Per Christian Hansen Pdf

This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms.