Numerical Methods For Inverse Problems

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Numerical Methods for Inverse Problems

Michel Kern
Numerical Methods for Inverse Problems Book PDF

Author : Michel Kern
Publisher : John Wiley & Sons
Page : 228 pages
File Size : 46,9 Mb
Release : 2016-03-31
Category : Mathematics
ISBN : 9781119136965

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Numerical Methods for Inverse Problems by Michel Kern Pdf

This book studies methods to concretely address inverse problems. An inverse problem arises when the causes that produced a given effect must be determined or when one seeks to indirectly estimate the parameters of a physical system. The author uses practical examples to illustrate inverse problems in physical sciences. He presents the techniques and specific methods chosen to solve inverse problems in a general domain of application, choosing to focus on a small number of methods that can be used in most applications. This book is aimed at readers with a mathematical and scientific computing background. Despite this, it is a book with a practical perspective. The methods described are applicable, have been applied, and are often illustrated by numerical examples.

Numerical Methods for Inverse Problems

Michel Kern
Numerical Methods for Inverse Problems Book PDF

Author : Michel Kern
Publisher : John Wiley & Sons
Page : 232 pages
File Size : 46,7 Mb
Release : 2016-06-07
Category : Mathematics
ISBN : 9781848218185

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Numerical Methods for Inverse Problems by Michel Kern Pdf

This book studies methods to concretely address inverse problems. An inverse problem arises when the causes that produced a given effect must be determined or when one seeks to indirectly estimate the parameters of a physical system. The author uses practical examples to illustrate inverse problems in physical sciences. He presents the techniques and specific methods chosen to solve inverse problems in a general domain of application, choosing to focus on a small number of methods that can be used in most applications. This book is aimed at readers with a mathematical and scientific computing background. Despite this, it is a book with a practical perspective. The methods described are applicable, have been applied, and are often illustrated by numerical examples.

Numerical Methods for Solving Inverse Problems of Mathematical Physics

A. A. Samarskii,Petr N. Vabishchevich
Numerical Methods for Solving Inverse Problems of Mathematical Physics Book PDF

Author : A. A. Samarskii,Petr N. Vabishchevich
Publisher : Walter de Gruyter
Page : 453 pages
File Size : 49,7 Mb
Release : 2008-08-27
Category : Mathematics
ISBN : 9783110205794

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Numerical Methods for Solving Inverse Problems of Mathematical Physics by A. A. Samarskii,Petr N. Vabishchevich Pdf

The main classes of inverse problems for equations of mathematical physics and their numerical solution methods are considered in this book which is intended for graduate students and experts in applied mathematics, computational mathematics, and mathematical modelling.

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 : 50,6 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.

Surveys on Solution Methods for Inverse Problems

David Colton,Heinz W. Engl,Alfred K. Louis,Joyce McLaughlin,William Rundell
Surveys on Solution Methods for Inverse Problems Book PDF

Author : David Colton,Heinz W. Engl,Alfred K. Louis,Joyce McLaughlin,William Rundell
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783709162965

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Surveys on Solution Methods for Inverse Problems by David Colton,Heinz W. Engl,Alfred K. Louis,Joyce McLaughlin,William Rundell Pdf

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.

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 : 55,8 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 9780898715507

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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.

Numerical Regularization for Atmospheric Inverse Problems

Adrian Doicu,Thomas Trautmann,Franz Schreier
Numerical Regularization for Atmospheric Inverse Problems Book PDF

Author : Adrian Doicu,Thomas Trautmann,Franz Schreier
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 40,6 Mb
Release : 2010-07-16
Category : Science
ISBN : 9783642054396

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Numerical Regularization for Atmospheric Inverse Problems by Adrian Doicu,Thomas Trautmann,Franz Schreier Pdf

The retrieval problems arising in atmospheric remote sensing belong to the class of the - called discrete ill-posed problems. These problems are unstable under data perturbations, and can be solved by numerical regularization methods, in which the solution is stabilized by taking additional information into account. The goal of this research monograph is to present and analyze numerical algorithms for atmospheric retrieval. The book is aimed at physicists and engineers with some ba- ground in numerical linear algebra and matrix computations. Although there are many practical details in this book, for a robust and ef?cient implementation of all numerical algorithms, the reader should consult the literature cited. The data model adopted in our analysis is semi-stochastic. From a practical point of view, there are no signi?cant differences between a semi-stochastic and a determin- tic framework; the differences are relevant from a theoretical point of view, e.g., in the convergence and convergence rates analysis. After an introductory chapter providing the state of the art in passive atmospheric remote sensing, Chapter 2 introduces the concept of ill-posedness for linear discrete eq- tions. To illustrate the dif?culties associated with the solution of discrete ill-posed pr- lems, we consider the temperature retrieval by nadir sounding and analyze the solvability of the discrete equation by using the singular value decomposition of the forward model matrix.

Computational Methods for Inverse Problems in Imaging

Marco Donatelli,Stefano Serra-Capizzano
Computational Methods for Inverse Problems in Imaging Book PDF

Author : Marco Donatelli,Stefano Serra-Capizzano
Publisher : Springer Nature
Page : 171 pages
File Size : 44,7 Mb
Release : 2019-11-26
Category : Mathematics
ISBN : 9783030328825

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Computational Methods for Inverse Problems in Imaging by Marco Donatelli,Stefano Serra-Capizzano Pdf

This book presents recent mathematical methods in the area of inverse problems in imaging with a particular focus on the computational aspects and applications. The formulation of inverse problems in imaging requires accurate mathematical modeling in order to preserve the significant features of the image. The book describes computational methods to efficiently address these problems based on new optimization algorithms for smooth and nonsmooth convex minimization, on the use of structured (numerical) linear algebra, and on multilevel techniques. It also discusses various current and challenging applications in fields such as astronomy, microscopy, and biomedical imaging. The book is intended for researchers and advanced graduate students interested in inverse problems and imaging.

Statistical and Computational Inverse Problems

Jari Kaipio,E. Somersalo
Statistical and Computational Inverse Problems Book PDF

Author : Jari Kaipio,E. Somersalo
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 41,8 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9780387271323

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Statistical and Computational Inverse Problems by Jari Kaipio,E. Somersalo Pdf

This book covers the statistical mechanics approach to computational solution of inverse problems, an innovative area of current research with very promising numerical results. The techniques are applied to a number of real world applications such as limited angle tomography, image deblurring, electical impedance tomography, and biomagnetic inverse problems. Contains detailed examples throughout and includes a chapter on case studies where such methods have been implemented in biomedical engineering.

Rank-Deficient and Discrete Ill-Posed Problems

Per Christian Hansen
Rank Deficient and Discrete Ill Posed Problems Book PDF

Author : Per Christian Hansen
Publisher : SIAM
Page : 259 pages
File Size : 53,7 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 9780898714036

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Rank-Deficient and Discrete Ill-Posed Problems by Per Christian Hansen Pdf

Here is an overview of modern computational stabilization methods for linear inversion, with applications to a variety of problems in audio processing, medical imaging, tomography, seismology, astronomy, and other areas. Rank-deficient problems involve matrices that are either exactly or nearly rank deficient. Such problems often arise in connection with noise suppression and other problems where the goal is to suppress unwanted disturbances of the given measurements. Discrete ill-posed problems arise in connection with the numerical treatment of inverse problems, where one typically wants to compute information about some interior properties using exterior measurements. Examples of inverse problems are image restoration and tomography, where one needs to improve blurred images or reconstruct pictures from raw data. This book describes, in a common framework, new and existing numerical methods for the analysis and solution of rank-deficient and discrete ill-posed problems. The emphasis is on insight into the stabilizing properties of the algorithms and on the efficiency and reliability of the computations. The setting is that of numerical linear algebra rather than abstract functional analysis, and the theoretical development is complemented with numerical examples and figures that illustrate the features of the various algorithms.

Numerical Treatment of Inverse Problems in Differential and Integral Equations

Deuflhard,Hairer
Numerical Treatment of Inverse Problems in Differential and Integral Equations Book PDF

Author : Deuflhard,Hairer
Publisher : Springer Science & Business Media
Page : 369 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468473247

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Numerical Treatment of Inverse Problems in Differential and Integral Equations by Deuflhard,Hairer Pdf

In many scientific or engineering applications, where ordinary differen tial equation (OOE),partial differential equation (POE), or integral equation (IE) models are involved, numerical simulation is in common use for prediction, monitoring, or control purposes. In many cases, however, successful simulation of a process must be preceded by the solution of the so-called inverse problem, which is usually more complex: given meas ured data and an associated theoretical model, determine unknown para meters in that model (or unknown functions to be parametrized) in such a way that some measure of the "discrepancy" between data and model is minimal. The present volume deals with the numerical treatment of such inverse probelms in fields of application like chemistry (Chap. 2,3,4, 7,9), molecular biology (Chap. 22), physics (Chap. 8,11,20), geophysics (Chap. 10,19), astronomy (Chap. 5), reservoir simulation (Chap. 15,16), elctrocardiology (Chap. 14), computer tomography (Chap. 21), and control system design (Chap. 12,13). In the actual computational solution of inverse problems in these fields, the following typical difficulties arise: (1) The evaluation of the sen sitivity coefficients for the model. may be rather time and storage con suming. Nevertheless these coefficients are needed (a) to ensure (local) uniqueness of the solution, (b) to estimate the accuracy of the obtained approximation of the solution, (c) to speed up the iterative solution of nonlinear problems. (2) Often the inverse problems are ill-posed. To cope with this fact in the presence of noisy or incomplete data or inev itable discretization errors, regularization techniques are necessary.

Inverse Problems and Applications

Larisa Beilina
Inverse Problems and Applications Book PDF

Author : Larisa Beilina
Publisher : Springer
Page : 164 pages
File Size : 55,5 Mb
Release : 2015-02-17
Category : Mathematics
ISBN : 9783319124995

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Inverse Problems and Applications by Larisa Beilina Pdf

​​This volume arose from the Third Annual Workshop on Inverse Problems, held in Stockholm on May 2-6, 2012. The proceedings present new analytical developments and numerical methods for solutions of inverse and ill-posed problems, which consistently pose complex challenges to the development of effective numerical methods. The book highlights recent research focusing on reliable numerical techniques for the solution of inverse problems, with relevance to a range of fields including acoustics, electromagnetics, optics, medical imaging, and geophysics. ​

Discrete Inverse Problems

Per Christian Hansen
Discrete Inverse Problems Book PDF

Author : Per Christian Hansen
Publisher : SIAM
Page : 220 pages
File Size : 45,7 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.

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 : 55,8 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.

Inverse Problems

Mathias Richter
Inverse Problems Book PDF

Author : Mathias Richter
Publisher : Birkhäuser
Page : 248 pages
File Size : 53,9 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.