Surveys On Solution Methods For Inverse Problems

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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 : 51,7 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.

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 : 42,8 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.

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 : 50,9 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.

Perspectives on Enclosure Methods

Ulrich Kulisch,Rudolf Lohner,Axel Facius
Perspectives on Enclosure Methods Book PDF

Author : Ulrich Kulisch,Rudolf Lohner,Axel Facius
Publisher : Springer Science & Business Media
Page : 368 pages
File Size : 40,8 Mb
Release : 2001-06-18
Category : Computers
ISBN : 3211835903

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Perspectives on Enclosure Methods by Ulrich Kulisch,Rudolf Lohner,Axel Facius Pdf

Enclosure methods and their applications have been developed to a high standard during the last decades. These methods guarantee the validity of the computed results. This means they are of the same standard as the rest of mathematics. The book deals with a wide variety of aspects of enclosure methods. All contributions follow the common goal to push the limits of enclosure methods forward. Topics that are treated include basic questions of arithmetic, proving conjectures, bounds for Krylow type linear system solvers, bounds for eigenvalues, the wrapping effect, algorithmic differencing, differential equations, finite element methods, application in robotics, and nonsmooth global optimization.

Multidisciplinary Methods for Analysis, Optimization and Control of Complex Systems

Vincenzo Capasso,Jacques Periaux
Multidisciplinary Methods for Analysis Optimization and Control of Complex Systems Book PDF

Author : Vincenzo Capasso,Jacques Periaux
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 52,7 Mb
Release : 2006-01-05
Category : Mathematics
ISBN : 9783540271673

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Multidisciplinary Methods for Analysis, Optimization and Control of Complex Systems by Vincenzo Capasso,Jacques Periaux Pdf

This book consists of lecture notes of a summer school named after the late Jacques Louis Lions. The summer school was designed to alert both Academia and Industry to the increasing role of multidisciplinary methods and tools for the design of complex products in various areas of socio-economic interest. This volume offers the reader a rare opportunity of being exposed to the presentation of real industrial and societal problems together with the relevant innovative methods used.

Regularization Methods in Banach Spaces

Thomas Schuster,Barbara Kaltenbacher,Bernd Hofmann,Kamil S. Kazimierski
Regularization Methods in Banach Spaces Book PDF

Author : Thomas Schuster,Barbara Kaltenbacher,Bernd Hofmann,Kamil S. Kazimierski
Publisher : Walter de Gruyter
Page : 296 pages
File Size : 50,8 Mb
Release : 2012-07-30
Category : Mathematics
ISBN : 9783110255720

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Regularization Methods in Banach Spaces by Thomas Schuster,Barbara Kaltenbacher,Bernd Hofmann,Kamil S. Kazimierski Pdf

Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of applications ranging from medical imaging and non-destructive testing via finance to systems biology. Many of these problems belong to the class of parameter identification problems in partial differential equations (PDEs) and thus are computationally demanding and mathematically challenging. Hence there is a substantial need for stable and efficient solvers for this kind of problems as well as for a rigorous convergence analysis of these methods. This monograph consists of five parts. Part I motivates the importance of developing and analyzing regularization methods in Banach spaces by presenting four applications which intrinsically demand for a Banach space setting and giving a brief glimpse of sparsity constraints. Part II summarizes all mathematical tools that are necessary to carry out an analysis in Banach spaces. Part III represents the current state-of-the-art concerning Tikhonov regularization in Banach spaces. Part IV about iterative regularization methods is concerned with linear operator equations and the iterative solution of nonlinear operator equations by gradient type methods and the iteratively regularized Gauß-Newton method. Part V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels.

Inverse Problems, Image Analysis, and Medical Imaging

M. Zuhair Nashed,Otmar Scherzer,AMS Special Session on Interaction of Inverse Problems
Inverse Problems Image Analysis and Medical Imaging Book PDF

Author : M. Zuhair Nashed,Otmar Scherzer,AMS Special Session on Interaction of Inverse Problems
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 53,8 Mb
Release : 2002
Category : Diagnostic imaging
ISBN : 9780821829790

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Inverse Problems, Image Analysis, and Medical Imaging by M. Zuhair Nashed,Otmar Scherzer,AMS Special Session on Interaction of Inverse Problems Pdf

This book contains the proceedings of the Special Session, Interaction of Inverse Problems and Image Analysis, held at the January 2001 meeting of the AMS in New Orleans, LA. The common thread among inverse problems, signal analysis, and image analysis is a canonical problem: recovering an object (function, signal, picture) from partial or indirect information about the object. Both inverse problems and imaging science have emerged in recent years as interdisciplinary research fields with profound applications in many areas of science, engineering, technology, and medicine. Research in inverse problems and image processing shows rich interaction with several areas of mathematics and strong links to signal processing, variational problems, applied harmonic analysis, and computational mathematics. This volume contains carefully referred and edited original research papers and high-level survey papers that provide overview and perspective on the interaction of inverse problems, image analysis, and medical imaging. The book is suitable for graduate students and researchers interested in signal and image processing and medical imaging.

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 : 46,9 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.

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 : 50,5 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 in Vibration

G.M.L. Gladwell
Inverse Problems in Vibration Book PDF

Author : G.M.L. Gladwell
Publisher : Springer Science & Business Media
Page : 484 pages
File Size : 41,6 Mb
Release : 2004-08-10
Category : Technology & Engineering
ISBN : 1402026706

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Inverse Problems in Vibration by G.M.L. Gladwell Pdf

In the first, 1986, edition of this book, inverse problems in vibration were interpreted strictly: problems concerning the reconstruction of a unique, undamped vibrating system, of a specified type, from specified vibratory behaviour, particularly specified natural frequencies and/or natural mode shapes. In this new edition the scope of the book has been widened to include topics such as isospectral systems- families of systems which all exhibit some specified behaviour; applications of the concept of Toda flow; new, non-classical approaches to inverse Sturm-Liouville problems; qualitative properties of the modes of some finite element models; damage identification. With its emphasis on analysis, on qualitative results, rather than on computation, the book will appeal to researchers in vibration theory, matrix analysis, differential and integral equations, matrix analysis, non-destructive testing, modal analysis, vibration isolation, etc. "This book is a necessary addition to the library of engineers and mathematicians working in vibration theory." Mathematical Reviews

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 : 732 pages
File Size : 42,8 Mb
Release : 2000-03-21
Category : Mathematics
ISBN : 9781482292985

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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, app

The Method of Approximate Inverse: Theory and Applications

Thomas Schuster
The Method of Approximate Inverse Theory and Applications Book PDF

Author : Thomas Schuster
Publisher : Springer
Page : 202 pages
File Size : 52,7 Mb
Release : 2007-04-26
Category : Mathematics
ISBN : 9783540712275

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The Method of Approximate Inverse: Theory and Applications by Thomas Schuster Pdf

This book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings. It demonstrates the performance and functionality of the method on several examples from medical imaging and non-destructive testing, such as computerized tomography, Doppler tomography, SONAR, X-ray diffractometry and thermoacoustic computerized tomography.

Transport Phenomena and Kinetic Theory

Carlo Cercignani,Ester Gabetta
Transport Phenomena and Kinetic Theory Book PDF

Author : Carlo Cercignani,Ester Gabetta
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 45,7 Mb
Release : 2007-12-03
Category : Science
ISBN : 9780817645540

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Transport Phenomena and Kinetic Theory by Carlo Cercignani,Ester Gabetta Pdf

The study of kinetic equations related to gases, semiconductors, photons, traffic flow, and other systems has developed rapidly in recent years because of its role as a mathematical tool in areas such as engineering, meteorology, biology, chemistry, materials science, nanotechnology, and pharmacy. Written by leading specialists in their respective fields, this book presents an overview of recent developments in the field of mathematical kinetic theory with a focus on modeling complex systems, emphasizing both mathematical properties and their physical meaning. Transport Phenomena and Kinetic Theory is an excellent self-study reference for graduate students, researchers, and practitioners working in pure and applied mathematics, mathematical physics, and engineering. The work may be used in courses or seminars on selected topics in transport phenomena or applications of the Boltzmann equation.

Computational Methods in Physics

Simon Širca,Martin Horvat
Computational Methods in Physics Book PDF

Author : Simon Širca,Martin Horvat
Publisher : Springer
Page : 880 pages
File Size : 41,6 Mb
Release : 2018-06-21
Category : Science
ISBN : 9783319786193

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Computational Methods in Physics by Simon Širca,Martin Horvat Pdf

This book is intended to help advanced undergraduate, graduate, and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues, as well as optimization of program execution speeds. Numerous examples are given throughout the chapters, followed by comprehensive end-of-chapter problems with a more pronounced physics background, while less stress is given to the explanation of individual algorithms. The readers are encouraged to develop a certain amount of skepticism and scrutiny instead of blindly following readily available commercial tools. The second edition has been enriched by a chapter on inverse problems dealing with the solution of integral equations, inverse Sturm-Liouville problems, as well as retrospective and recovery problems for partial differential equations. The revised text now includes an introduction to sparse matrix methods, the solution of matrix equations, and pseudospectra of matrices; it discusses the sparse Fourier, non-uniform Fourier and discrete wavelet transformations, the basics of non-linear regression and the Kolmogorov-Smirnov test; it demonstrates the key concepts in solving stiff differential equations and the asymptotics of Sturm-Liouville eigenvalues and eigenfunctions. Among other updates, it also presents the techniques of state-space reconstruction, methods to calculate the matrix exponential, generate random permutations and compute stable derivatives.

The Factorization Method for Inverse Problems

Andreas Kirsch,Natalia Grinberg
The Factorization Method for Inverse Problems Book PDF

Author : Andreas Kirsch,Natalia Grinberg
Publisher : Oxford University Press
Page : 216 pages
File Size : 51,8 Mb
Release : 2008
Category : Mathematics
ISBN : 9780199213535

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The Factorization Method for Inverse Problems by Andreas Kirsch,Natalia Grinberg Pdf

The 'factorization method', discovered by Professor Kirsch, is a relatively new method for solving certain types of inverse scattering problems and problems in tomography. The text introduces the reader to this promising approach and discusses the wide applicability of this method by choosing typical examples.