An Introduction to the Mathematical Theory of Inverse Problems

An Introduction to the Mathematical Theory of Inverse Problems
Title An Introduction to the Mathematical Theory of Inverse Problems PDF eBook
Author Andreas Kirsch
Publisher Springer Science & Business Media
Pages 314
Release 2011-03-24
Genre Mathematics
ISBN 1441984747

Download An Introduction to the Mathematical Theory of Inverse Problems Book in PDF, Epub and Kindle

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.

The Factorization Method for Inverse Problems

The Factorization Method for Inverse Problems
Title The Factorization Method for Inverse Problems PDF eBook
Author Andreas Kirsch
Publisher Oxford University Press, USA
Pages 216
Release 2008
Genre Mathematics
ISBN 0199213534

Download The Factorization Method for Inverse Problems Book in PDF, Epub and Kindle

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.

A Taste of Inverse Problems

A Taste of Inverse Problems
Title A Taste of Inverse Problems PDF eBook
Author Martin Hanke
Publisher SIAM
Pages 171
Release 2017-01-01
Genre Mathematics
ISBN 1611974933

Download A Taste of Inverse Problems Book in PDF, Epub and Kindle

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.

The Factorization Method for Inverse Scattering from Periodic Inhomogeneous Media

The Factorization Method for Inverse Scattering from Periodic Inhomogeneous Media
Title The Factorization Method for Inverse Scattering from Periodic Inhomogeneous Media PDF eBook
Author Kai Sandfort
Publisher KIT Scientific Publishing
Pages 168
Release 2014-10-16
Genre Mathematics
ISBN 3866445504

Download The Factorization Method for Inverse Scattering from Periodic Inhomogeneous Media Book in PDF, Epub and Kindle

This book addresses the identification of the shape of penetrable periodic media by means of scattered time-harmonic waves. Mathematically, this is about the determination of the support of a function which occurs in the governing equations. Our theoretical analysis shows that this problem can be strictly solved for acoustic as well as for electromagnetic radiation by the so-called Factorization Method. We apply this method to reconstruct a couple of media from numerically simulated field data.

Discrete Inverse Problems

Discrete Inverse Problems
Title Discrete Inverse Problems PDF eBook
Author Per Christian Hansen
Publisher SIAM
Pages 220
Release 2010-01-01
Genre Mathematics
ISBN 089871883X

Download Discrete Inverse Problems Book in PDF, Epub and Kindle

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.

Advances in Inverse Problems for Partial Differential Equations

Advances in Inverse Problems for Partial Differential Equations
Title Advances in Inverse Problems for Partial Differential Equations PDF eBook
Author Dinh-Liem Nguyen
Publisher American Mathematical Society
Pages 218
Release 2023-04-12
Genre Mathematics
ISBN 1470469685

Download Advances in Inverse Problems for Partial Differential Equations Book in PDF, Epub and Kindle

This volume contains the proceedings of two AMS Special Sessions “Recent Developments on Analysis and Computation for Inverse Problems for PDEs,” virtually held on March 13–14, 2021, and “Recent Advances in Inverse Problems for Partial Differential Equations,” virtually held on October 23–24, 2021. The papers in this volume focus on new results on numerical methods for various inverse problems arising in electrical impedance tomography, inverse scattering in radar and optics problems, reconstruction of initial conditions, control of acoustic fields, and stock price forecasting. The authors studied iterative and non-iterative approaches such as optimization-based, globally convergent, sampling, and machine learning-based methods. The volume provides an interesting source on advances in computational inverse problems for partial differential equations.

Optimization and Regularization for Computational Inverse Problems and Applications

Optimization and Regularization for Computational Inverse Problems and Applications
Title Optimization and Regularization for Computational Inverse Problems and Applications PDF eBook
Author Yanfei Wang
Publisher Springer Science & Business Media
Pages 354
Release 2011-06-29
Genre Mathematics
ISBN 3642137423

Download Optimization and Regularization for Computational Inverse Problems and Applications Book in PDF, Epub and Kindle

"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.