Inverse Problems And 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 : 52,5 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

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 : 53,9 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 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 : 47,7 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

Inverse Problems

Mathias Richter
Inverse Problems Book PDF

Author : Mathias Richter
Publisher : Birkhäuser
Page : 248 pages
File Size : 42,6 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.

Large Scale Inverse Problems

Mike Cullen,Melina A Freitag,Stefan Kindermann,Robert Scheichl
Large Scale Inverse Problems Book PDF

Author : Mike Cullen,Melina A Freitag,Stefan Kindermann,Robert Scheichl
Publisher : Walter de Gruyter
Page : 216 pages
File Size : 42,5 Mb
Release : 2013-08-29
Category : Mathematics
ISBN : 9783110282269

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Large Scale Inverse Problems by Mike Cullen,Melina A Freitag,Stefan Kindermann,Robert Scheichl Pdf

This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. Thiscollection of surveyarticlesfocusses onthe large inverse problems commonly arising in simulation and forecasting in the earth sciences. For example, operational weather forecasting models have between 107 and 108 degrees of freedom. Even so, these degrees of freedom represent grossly space-time averaged properties of the atmosphere. Accurate forecasts require accurate initial conditions. With recent developments in satellite data, there are between 106 and 107 observations each day. However, while these also represent space-time averaged properties, the averaging implicit in the measurements is quite different from that used in the models. In atmosphere and ocean applications, there is a physically-based model available which can be used to regularise the problem. We assume that there is a set of observations with known error characteristics available over a period of time. The basic deterministic technique is to fit a model trajectory to the observations over a period of time to within the observation error. Since the model is not perfect the model trajectory has to be corrected, which defines the data assimilation problem. The stochastic view can be expressed by using an ensemble of model trajectories, and calculating corrections to both the mean value and the spread which allow the observations to be fitted by each ensemble member. In other areas of earth science, only the structure of the model formulation itself is known and the aim is to use the past observation history to determine the unknown model parameters. The book records the achievements of Workshop2 "Large-Scale Inverse Problems and Applications in the Earth Sciences". Itinvolves experts in the theory of inverse problems together with experts working on both theoretical and practical aspects of the techniques by which large inverse problems arise in the earth sciences.

Inside Out

Gunther Uhlmann
Inside Out Book PDF

Author : Gunther Uhlmann
Publisher : Cambridge University Press
Page : 424 pages
File Size : 41,8 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 : 46,5 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.

Inverse Problems

Alexander G. Ramm
Inverse Problems Book PDF

Author : Alexander G. Ramm
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 53,8 Mb
Release : 2005-12-19
Category : Technology & Engineering
ISBN : 9780387232188

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Inverse Problems by Alexander G. Ramm Pdf

Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.

Inverse Problems and Applications

Gunther Uhlmann
Inverse Problems and Applications Book PDF

Author : Gunther Uhlmann
Publisher : Cambridge University Press
Page : 593 pages
File Size : 51,6 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.

Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems

Mourad Bellassoued,Masahiro Yamamoto
Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems Book PDF

Author : Mourad Bellassoued,Masahiro Yamamoto
Publisher : Springer
Page : 260 pages
File Size : 53,8 Mb
Release : 2017-11-23
Category : Mathematics
ISBN : 9784431566007

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Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems by Mourad Bellassoued,Masahiro Yamamoto Pdf

This book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions. The formulation is different from that of Dirichlet-to-Neumann maps and can often prove the global uniqueness and Lipschitz stability even with a single measurement. These types of inverse problems include coefficient inverse problems of determining physical parameters in inhomogeneous media that appear in many applications related to electromagnetism, elasticity, and related phenomena. Although the methodology was created in 1981 by Bukhgeim and Klibanov, its comprehensive development has been accomplished only recently. In spite of the wide applicability of the method, there are few monographs focusing on combined accounts of Carleman estimates and applications to inverse problems. The aim in this book is to fill that gap. The basic tool is Carleman estimates, the theory of which has been established within a very general framework, so that the method using Carleman estimates for inverse problems is misunderstood as being very difficult. The main purpose of the book is to provide an accessible approach to the methodology. To accomplish that goal, the authors include a direct derivation of Carleman estimates, the derivation being based essentially on elementary calculus working flexibly for various equations. Because the inverse problem depends heavily on respective equations, too general and abstract an approach may not be balanced. Thus a direct and concrete means was chosen not only because it is friendly to readers but also is much more relevant. By practical necessity, there is surely a wide range of inverse problems and the method delineated here can solve them. The intention is for readers to learn that method and then apply it to solving new inverse problems.

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 : 46,7 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.

Optimization and Regularization for Computational Inverse Problems and Applications

Yanfei Wang,Anatoly G. Yagola,Changchun Yang
Optimization and Regularization for Computational Inverse Problems and Applications Book PDF

Author : Yanfei Wang,Anatoly G. Yagola,Changchun Yang
Publisher : Springer
Page : 400 pages
File Size : 43,9 Mb
Release : 2011-01-04
Category : Mathematics
ISBN : 3642137415

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Optimization and Regularization for Computational Inverse Problems and Applications by Yanfei Wang,Anatoly G. Yagola,Changchun Yang Pdf

"Optimization and Regularization for Computational Inverse Problems and Applications" focuses on advances in inversion theory and recent developments with practical applications, particularly emphasizing the combination of optimization and regularization for solving inverse problems. This book covers both the methods, including standard regularization theory, Fejer processes for linear and nonlinear problems, the balancing principle, extrapolated regularization, nonstandard regularization, nonlinear gradient method, the nonmonotone gradient method, subspace method and Lie group method; and the practical applications, such as the reconstruction problem for inverse scattering, molecular spectra data processing, quantitative remote sensing inversion, seismic inversion using the Lie group method, and the gravitational lensing problem. Scientists, researchers and engineers, as well as graduate students engaged in applied mathematics, engineering, geophysics, medical science, image processing, remote sensing and atmospheric science will benefit from this book. Dr. Yanfei Wang is a Professor at the Institute of Geology and Geophysics, Chinese Academy of Sciences, China. Dr. Sc. Anatoly G. Yagola is a Professor and Assistant Dean of the Physical Faculty, Lomonosov Moscow State University, Russia. Dr. Changchun Yang is a Professor and Vice Director of the Institute of Geology and Geophysics, Chinese Academy of Sciences, China.

A Taste of Inverse Problems

Martin Hanke
A Taste of Inverse Problems Book PDF

Author : Martin Hanke
Publisher : SIAM
Page : 171 pages
File Size : 42,5 Mb
Release : 2017-01-01
Category : Mathematics
ISBN : 9781611974935

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A Taste of Inverse Problems by Martin Hanke Pdf

Inverse problems need to be solved in order to properly interpret indirect measurements. Often, inverse problems are ill-posed and sensitive to data errors. Therefore one has to incorporate some sort of regularization to reconstruct significant information from the given data. A Taste of Inverse Problems: Basic Theory and Examples?presents the main achievements that have emerged in regularization theory over the past 50 years, focusing on linear ill-posed problems and the development of methods that can be applied to them. Some of this material has previously appeared only in journal articles. This book rigorously discusses state-of-the-art inverse problems theory, focusing on numerically relevant aspects and omitting subordinate generalizations; presents diverse real-world applications, important test cases, and possible pitfalls; and treats these applications with the same rigor and depth as the theory.

Fixed-Point Algorithms for Inverse Problems in Science and Engineering

Heinz H. Bauschke,Regina S. Burachik,Patrick L. Combettes,Veit Elser,D. Russell Luke,Henry Wolkowicz
Fixed Point Algorithms for Inverse Problems in Science and Engineering Book PDF

Author : Heinz H. Bauschke,Regina S. Burachik,Patrick L. Combettes,Veit Elser,D. Russell Luke,Henry Wolkowicz
Publisher : Springer Science & Business Media
Page : 409 pages
File Size : 46,8 Mb
Release : 2011-05-27
Category : Mathematics
ISBN : 9781441995698

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Fixed-Point Algorithms for Inverse Problems in Science and Engineering by Heinz H. Bauschke,Regina S. Burachik,Patrick L. Combettes,Veit Elser,D. Russell Luke,Henry Wolkowicz Pdf

"Fixed-Point Algorithms for Inverse Problems in Science and Engineering" presents some of the most recent work from top-notch researchers studying projection and other first-order fixed-point algorithms in several areas of mathematics and the applied sciences. The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems. This book incorporates diverse perspectives from broad-ranging areas of research including, variational analysis, numerical linear algebra, biotechnology, materials science, computational solid-state physics, and chemistry. Topics presented include: Theory of Fixed-point algorithms: convex analysis, convex optimization, subdifferential calculus, nonsmooth analysis, proximal point methods, projection methods, resolvent and related fixed-point theoretic methods, and monotone operator theory. Numerical analysis of fixed-point algorithms: choice of step lengths, of weights, of blocks for block-iterative and parallel methods, and of relaxation parameters; regularization of ill-posed problems; numerical comparison of various methods. Areas of Applications: engineering (image and signal reconstruction and decompression problems), computer tomography and radiation treatment planning (convex feasibility problems), astronomy (adaptive optics), crystallography (molecular structure reconstruction), computational chemistry (molecular structure simulation) and other areas. Because of the variety of applications presented, this book can easily serve as a basis for new and innovated research and collaboration.

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 : 43,7 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.