Inverse Methods

Author : Albert Tarantola
Publisher : SIAM
Page : 349 pages
File Size : 43,6 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.

Author : Curtis R. Vogel
Publisher : SIAM
Page : 183 pages
File Size : 50,6 Mb
Release : 2002
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.

Author : Clive D. Rodgers
Publisher : World Scientific
Page : 256 pages
File Size : 41,5 Mb
Release : 2000
Category : Science
ISBN : 9789810227401

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Inverse Methods for Atmospheric Sounding by Clive D. Rodgers Pdf

Annotation Rodgers (U. of Oxford) provides graduate students and other researchers a background to the inverse problem and its solution, with applications relating to atmospheric measurements. He introduces the stages in the reverse order than the usual approach in order to develop the learner's intuition about the nature of the inverse problem. Annotation copyrighted by Book News, Inc., Portland, OR.

Author : Carl Wunsch
Publisher : Cambridge University Press
Page : 466 pages
File Size : 50,7 Mb
Release : 1996-06-13
Category : Mathematics
ISBN : 0521480906

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The Ocean Circulation Inverse Problem by Carl Wunsch Pdf

This book addresses the problem of inferring the state of the ocean circulation, from a mathematical perspective.

Author : Michel Kern
Publisher : John Wiley & Sons
Page : 232 pages
File Size : 55,5 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.

Author : Wolfgang-M. Boerner,Hans Brand,Leonard A. Cram,Dag T. Gjessing,Arthur K. Jordan,Wolfgang Keydel,Günther Schwierz,Martin Vogel
Publisher : Springer Science & Business Media
Page : 662 pages
File Size : 46,8 Mb
Release : 2013-11-21
Category : Science
ISBN : 9789400952713

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Inverse Methods in Electromagnetic Imaging by Wolfgang-M. Boerner,Hans Brand,Leonard A. Cram,Dag T. Gjessing,Arthur K. Jordan,Wolfgang Keydel,Günther Schwierz,Martin Vogel Pdf

In recent years, there has been an increased interest in the use of polarization effects for radar and electromagnetic imaging problems (References 1, 2, and 3). The problem of electro magnetic imaging can be divided into the following areas: (1) Propagation of the Stokes' vector from the transmitter to the target region through various atmospheric conditions (rain, dust, fog, clouds, turbulence, etc.). (2) Scattering of the Stokes' vector from the object. (3) Scattering of the Stokes' vector from the rough surface, terrain, and the volume scattering. (4) Propagation of the Stokes' vector from the target region to the receiver. (5) The characteristics of the receiver relating the Stokes' vector to the output. The propagation characteristics of the Stokes' vector through various media can be described by the equation of transfer. Even though the scalar equation of transfer has been studied extensively in the past, the vector equation of transfer has not received as much attention. In recent years, however, a need for further study of the vector radiative transfer theory has become increasingly evident and several important studies have been reported. This paper presents a general formulation of the vector theory of radiative transfer under general anisotropic scattering conditions. Some useful solutions are also presented 4 8 for several practical situations. - 2. GENERAL FORMULATION OF VECTOR RADIATIVE TRANSFER THEORY Let us consider the plane-parallel problem Shovlll in Figure 1.

Author : Prasad Kasibhatla
Publisher : American Geophysical Union
Page : 321 pages
File Size : 52,7 Mb
Release : 2000-01-10
Category : Mathematics
ISBN : 9780875900971

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Inverse Methods in Global Biogeochemical Cycles by Prasad Kasibhatla Pdf

The CD-ROM contains the code and data files for the Exercises outlined in the paper by Rayner, et at., (p. 81-106).

Author : David Colton,Heinz W. Engl,Alfred K. Louis,Joyce McLaughlin,William Rundell
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 55,8 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.

Author : Marco Donatelli,Stefano Serra-Capizzano
Publisher : Springer Nature
Page : 171 pages
File Size : 50,9 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.

Author : Richard C. Aster,Brian Borchers,Clifford H. Thurber
Publisher : Elsevier
Page : 404 pages
File Size : 51,9 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

Author : Christine Allison Doughty
Publisher : Unknown
Page : 564 pages
File Size : 42,8 Mb
Release : 1995
Category : Fractals
ISBN : UCAL:C3389125

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Estimation of Hydrologic Properties of Heterogeneous Geologic Media with an Inverse Method Based on Iterated Function Systems by Christine Allison Doughty Pdf

Author : Xudong Chen
Publisher : John Wiley & Sons
Page : 325 pages
File Size : 54,7 Mb
Release : 2018-07-18
Category : Science
ISBN : 9781119311980

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Computational Methods for Electromagnetic Inverse Scattering by Xudong Chen Pdf

A comprehensive and updated overview of the theory, algorithms and applications of for electromagnetic inverse scattering problems Offers the recent and most important advances in inverse scattering grounded in fundamental theory, algorithms and practical engineering applications Covers the latest, most relevant inverse scattering techniques like signal subspace methods, time reversal, linear sampling, qualitative methods, compressive sensing, and noniterative methods Emphasizes theory, mathematical derivation and physical insights of various inverse scattering problems Written by a leading expert in the field

Author : Yuan Jiang
Publisher : KIT Scientific Publishing
Page : 138 pages
File Size : 42,6 Mb
Release : 2014-08-13
Category : Technology & Engineering
ISBN : 9783866444867

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Solving the Inverse Problem of Electrocardiography in a Realistic Environment by Yuan Jiang Pdf

Heart disease is a leading cause of death worldwide. Straightforward information about the cardiac electrophysiology can help to improve the quality of diagnosis of heart diseases. The inverse problem of electrocardiography and the intracardiac catheter measurement are two ways to get access to the electrophysiology in the heart. In this thesis six research topics related to these two techniques are included.

Author : V. A. Yurko
Publisher : VSP
Page : 324 pages
File Size : 46,5 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 9067643556

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Method of Spectral Mappings in the Inverse Problem Theory by V. A. Yurko Pdf

Inverse problems of spectral analysis consist in recovering operators from their spectral characteristics. Such problems often appear in mathematics, mechanics, physics, electronics, geophysics, meteorology and other branches of natural science. This monograph deals with inverse problems of spectral analysis for ordinary differential equations and aims to present the main results on inverse spectral problems using the so-called method of spectral mappings, which is one of the main tools in inverse spectral theory.The book consists of three chapters and opens with the method of spectral mappings, presented in the simplest version for the Sturm-Liouville operator. The second chapter deals with the inverse problem of recovering higher-order differential operators of the form, on the half-line and on a finite interval. In this chapter the author introduces the so-called Weyl matrix, which is a generalization of the classical Weyl function for the selfadjoint second-order differential operator. The last chapter contains a study on inverse spectral problems for differential equations with nonlinear dependence on the spectral parameter.This monograph will be of value and interest to specialists in the field of inverse problems for differential equations.

Author : Andreas Kirsch
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 44,8 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.