Inverse Problems In The Mathematical Sciences

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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 : 47,9 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.

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 : 41,7 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.

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 : 55,9 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.

Inside Out

Gunther Uhlmann
Inside Out Book PDF

Author : Gunther Uhlmann
Publisher : Cambridge University Press
Page : 424 pages
File Size : 51,9 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.

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 : 55,5 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

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 : 50,7 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.

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 : 44,8 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.

Inverse Problems for Partial Differential Equations

Victor Isakov
Inverse Problems for Partial Differential Equations Book PDF

Author : Victor Isakov
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 43,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781489900302

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Inverse Problems for Partial Differential Equations by Victor Isakov Pdf

A comprehensive description of the current theoretical and numerical aspects of inverse problems in partial differential equations. Applications include recovery of inclusions from anomalies of their gravity fields, reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurement. By presenting the data in a readable and informative manner, the book introduces both scientific and engineering researchers as well as graduate students to the significant work done in this area in recent years, relating it to broader themes in mathematical analysis.

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 : 51,6 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.

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 : 50,8 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 and Applications

Gunther Uhlmann
Inverse Problems and Applications Book PDF

Author : Gunther Uhlmann
Publisher : Cambridge University Press
Page : 593 pages
File Size : 54,6 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.

Inverse Problems and Related Topics

Jin Cheng,Shuai Lu,Masahiro Yamamoto
Inverse Problems and Related Topics Book PDF

Author : Jin Cheng,Shuai Lu,Masahiro Yamamoto
Publisher : Springer Nature
Page : 310 pages
File Size : 41,7 Mb
Release : 2020-02-04
Category : Mathematics
ISBN : 9789811515927

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Inverse Problems and Related Topics by Jin Cheng,Shuai Lu,Masahiro Yamamoto Pdf

This volume contains 13 chapters, which are extended versions of the presentations at International Conference on Inverse Problems at Fudan University, Shanghai, China, October 12-14, 2018, in honor of Masahiro Yamamoto on the occasion of his 60th anniversary. The chapters are authored by world-renowned researchers and rising young talents, and are updated accounts of various aspects of the researches on inverse problems. The volume covers theories of inverse problems for partial differential equations, regularization methods, and related topics from control theory. This book addresses a wide audience of researchers and young post-docs and graduate students who are interested in mathematical sciences as well as mathematics.

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 : 47,7 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.

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 : 43,8 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 : 45,9 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.