An Introduction To Inverse Problems With Applications

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An Introduction to Inverse Problems with Applications

Francisco Duarte Moura Neto,Antônio José da Silva Neto
An Introduction to Inverse Problems with Applications Book PDF

Author : Francisco Duarte Moura Neto,Antônio José da Silva Neto
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 51,7 Mb
Release : 2012-09-14
Category : Mathematics
ISBN : 9783642325564

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An Introduction to Inverse Problems with Applications by Francisco Duarte Moura Neto,Antônio José da Silva Neto Pdf

Computational engineering/science uses a blend of applications, mathematical models and computations. Mathematical models require accurate approximations of their parameters, which are often viewed as solutions to inverse problems. Thus, the study of inverse problems is an integral part of computational engineering/science. This book presents several aspects of inverse problems along with needed prerequisite topics in numerical analysis and matrix algebra. If the reader has previously studied these prerequisites, then one can rapidly move to the inverse problems in chapters 4-8 on image restoration, thermal radiation, thermal characterization and heat transfer. “This text does provide a comprehensive introduction to inverse problems and fills a void in the literature”. Robert E White, Professor of Mathematics, North Carolina State University

Inverse Problems with Applications in Science and Engineering

Daniel Lesnic
Inverse Problems with Applications in Science and Engineering Book PDF

Author : Daniel Lesnic
Publisher : CRC Press
Page : 360 pages
File Size : 40,5 Mb
Release : 2021-11-10
Category : Mathematics
ISBN : 9780429683251

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Inverse Problems with Applications in Science and Engineering by Daniel Lesnic Pdf

Driven by the advancement of industrial mathematics and the need for impact case studies, Inverse Problems with Applications in Science and Engineering thoroughly examines the state-of-the-art of some representative classes of inverse and ill-posed problems for partial differential equations (PDEs). The natural practical applications of this examination arise in heat transfer, electrostatics, porous media, acoustics, fluid and solid mechanics – all of which are addressed in this text. Features: Covers all types of PDEs — namely, elliptic (Laplace’s, Helmholtz, modified Helmholtz, biharmonic and Stokes), parabolic (heat, convection, reaction and diffusion) and hyperbolic (wave) Excellent reference for post-graduates and researchers in mathematics, engineering and any other scientific discipline that deals with inverse problems Contains both theory and numerical algorithms for solving all types of inverse and ill-posed problems

Introduction to Inverse Problems for Differential Equations

Alemdar Hasanov Hasanoğlu,Vladimir G. Romanov
Introduction to Inverse Problems for Differential Equations Book PDF

Author : Alemdar Hasanov Hasanoğlu,Vladimir G. Romanov
Publisher : Springer
Page : 261 pages
File Size : 41,6 Mb
Release : 2017-07-31
Category : Mathematics
ISBN : 9783319627977

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Introduction to Inverse Problems for Differential Equations by Alemdar Hasanov Hasanoğlu,Vladimir G. Romanov Pdf

This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering. The book’s content, especially in the Introduction and Part I, is self-contained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations. In turn, the second part of the book consists of six nearly-independent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here are based on the basic and commonly used mathematical models governed by PDEs. These chapters describe not only these inverse problems, but also main inversion methods and techniques. Since the most distinctive features of any inverse problems related to PDEs are hidden in the properties of the corresponding solutions to direct problems, special attention is paid to the investigation of these properties.

An Introduction to Inverse Problems with Applications

Francisco Duarte Moura Neto,Antônio José da Silva Neto
An Introduction to Inverse Problems with Applications Book PDF

Author : Francisco Duarte Moura Neto,Antônio José da Silva Neto
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 41,7 Mb
Release : 2012-09-14
Category : Technology & Engineering
ISBN : 9783642325571

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An Introduction to Inverse Problems with Applications by Francisco Duarte Moura Neto,Antônio José da Silva Neto Pdf

Computational engineering/science uses a blend of applications, mathematical models and computations. Mathematical models require accurate approximations of their parameters, which are often viewed as solutions to inverse problems. Thus, the study of inverse problems is an integral part of computational engineering/science. This book presents several aspects of inverse problems along with needed prerequisite topics in numerical analysis and matrix algebra. If the reader has previously studied these prerequisites, then one can rapidly move to the inverse problems in chapters 4-8 on image restoration, thermal radiation, thermal characterization and heat transfer. “This text does provide a comprehensive introduction to inverse problems and fills a void in the literature”. Robert E White, Professor of Mathematics, North Carolina State University

Inverse Problems

Mathias Richter
Inverse Problems Book PDF

Author : Mathias Richter
Publisher : Birkhäuser
Page : 248 pages
File Size : 49,8 Mb
Release : 2016-11-24
Category : Mathematics
ISBN : 9783319483849

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Inverse Problems by Mathias Richter Pdf

The overall goal of the book is to provide access to the regularized solution of inverse problems relevant in geophysics without requiring more mathematical knowledge than is taught in undergraduate math courses for scientists and engineers. From abstract analysis only the concept of functions as vectors is needed. Function spaces are introduced informally in the course of the text, when needed. Additionally, a more detailed, but still condensed introduction is given in Appendix B. A second goal is to elaborate the single steps to be taken when solving an inverse problem: discretization, regularization and practical solution of the regularized optimization problem. These steps are shown in detail for model problems from the fields of inverse gravimetry and seismic tomography. The intended audience is mathematicians, physicists and engineers having a good working knowledge of linear algebra and analysis at the upper undergraduate level.

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 : 49,7 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.

Inverse Problems

Mathias Richter
Inverse Problems Book PDF

Author : Mathias Richter
Publisher : Springer Nature
Page : 281 pages
File Size : 55,7 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.

Inside Out

Gunther Uhlmann
Inside Out Book PDF

Author : Gunther Uhlmann
Publisher : Cambridge University Press
Page : 424 pages
File Size : 46,6 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.

Regularization of Inverse Problems

Heinz Werner Engl,Martin Hanke,A. Neubauer
Regularization of Inverse Problems Book PDF

Author : Heinz Werner Engl,Martin Hanke,A. Neubauer
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 54,8 Mb
Release : 2000-03-31
Category : Mathematics
ISBN : 0792361407

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Regularization of Inverse Problems by Heinz Werner Engl,Martin Hanke,A. Neubauer Pdf

This book is devoted to the mathematical theory of regularization methods and gives an account of the currently available results about regularization methods for linear and nonlinear ill-posed problems. Both continuous and iterative regularization methods are considered in detail with special emphasis on the development of parameter choice and stopping rules which lead to optimal convergence rates.

Linear and Nonlinear Inverse Problems with Practical Applications

Jennifer L. Mueller,Samuli Siltanen
Linear and Nonlinear Inverse Problems with Practical Applications Book PDF

Author : Jennifer L. Mueller,Samuli Siltanen
Publisher : SIAM
Page : 349 pages
File Size : 43,7 Mb
Release : 2012-11-30
Category : Mathematics
ISBN : 9781611972337

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Linear and Nonlinear Inverse Problems with Practical Applications by Jennifer L. Mueller,Samuli Siltanen Pdf

Inverse problems arise in practical applications whenever there is a need to interpret indirect measurements. This book explains how to identify ill-posed inverse problems arising in practice and gives a hands-on guide to designing computational solution methods for them, with related codes on an accompanying website. The guiding linear inversion examples are the problem of image deblurring, x-ray tomography, and backward parabolic problems, including heat transfer. A thorough treatment of electrical impedance tomography is used as the guiding nonlinear inversion example which combines the analytic-geometric research tradition and the regularization-based school of thought in a fruitful manner. This book is complete with exercises and project topics, making it ideal as a classroom textbook or self-study guide for graduate and advanced undergraduate students in mathematics, engineering or physics who wish to learn about computational inversion. It also acts as a useful guide for researchers who develop inversion techniques in high-tech industry.

Inverse Problems and Applications

Gunther Uhlmann
Inverse Problems and Applications Book PDF

Author : Gunther Uhlmann
Publisher : Cambridge University Press
Page : 593 pages
File Size : 54,7 Mb
Release : 2013
Category : Mathematics
ISBN : 9781107032019

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Inverse Problems and Applications by Gunther Uhlmann Pdf

Inverse problems lie at the heart of contemporary scientific inquiry and technological development. Applications include a variety of medical and other imaging techniques, which are used for early detection of cancer and pulmonary edema, location of oil and mineral deposits in the Earth's interior, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes, and modeling in the life sciences among others. The expository survey essays in this book describe recent developments in inverse problems and imaging, including hybrid or couple-physics methods arising in medical imaging, Calderon's problem and electrical impedance tomography, inverse problems arising in global seismology and oil exploration, inverse spectral problems, and the study of asymptotically hyperbolic spaces. It is suitable for graduate students and researchers interested in inverse problems and their applications.

An Introduction to Inverse Scattering and Inverse Spectral Problems

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

Author : Khosrow Chadan,David Colton,Lassi P?iv?rinta,William Rundell
Publisher : SIAM
Page : 206 pages
File Size : 49,5 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 9780898713879

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

An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems

Luis Tenorio
An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems Book PDF

Author : Luis Tenorio
Publisher : SIAM
Page : 275 pages
File Size : 46,7 Mb
Release : 2017-07-06
Category : Mathematics
ISBN : 9781611974911

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An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems by Luis Tenorio Pdf

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.

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 : 53,9 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

Inverse Problems in Groundwater Modeling

Ne-Zheng Sun
Inverse Problems in Groundwater Modeling Book PDF

Author : Ne-Zheng Sun
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 49,8 Mb
Release : 2013-04-17
Category : Science
ISBN : 9789401719704

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Inverse Problems in Groundwater Modeling by Ne-Zheng Sun Pdf

... A diskette with the updated programme of Appendix C and examples is available through the author at a small fee. email: [email protected] fax: 1--310--825--5435 ... This book systematically discusses basic concepts, theory, solution methods and applications of inverse problems in groundwater modeling. It is the first book devoted to this subject. The inverse problem is defined and solved in both deterministic and statistic frameworks. Various direct and indirect methods are discussed and compared. As a useful tool, the adjoint state method and its applications are given in detail. For a stochastic field, the maximum likelihood estimation and co-kriging techniques are used to estimate unknown parameters. The ill-posed problem of inverse solution is highlighted through the whole book. The importance of data collection strategy is specially emphasized. Besides the classical design criteria, the relationships between decision making, prediction, parameter identification and experimental design are considered from the point of view of extended identifiabilities. The problem of model structure identification is also considered. This book can be used as a textbook for graduate students majoring in hydrogeology or related subjects. It is also a reference book for hydrogeologists, petroleum engineers, environmental engineers, mining engineers and applied mathematicians.