Inverse Problems Tikhonov Theory And Algorithms
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Author | : Kazufumi Ito |
Publisher | : World Scientific |
Total Pages | : 330 |
Release | : 2014-08-28 |
Genre | : Mathematics |
ISBN | : 9814596213 |
Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a valuable contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are discussed in detail. The mathematical theory focuses on nonsmooth Tikhonov regularization for linear and nonlinear inverse problems. The computational methods include nonsmooth optimization algorithms, direct inversion methods and uncertainty quantification via Bayesian inference.The book offers a comprehensive treatment of modern techniques, and seamlessly blends regularization theory with computational methods, which is essential for developing accurate and efficient inversion algorithms for many practical inverse problems.It demonstrates many current developments in the field of computational inversion, such as value function calculus, augmented Tikhonov regularization, multi-parameter Tikhonov regularization, semismooth Newton method, direct sampling method, uncertainty quantification and approximate Bayesian inference. It is written for graduate students and researchers in mathematics, natural science and engineering.
Author | : Curtis R. Vogel |
Publisher | : SIAM |
Total Pages | : 195 |
Release | : 2002-01-01 |
Genre | : Mathematics |
ISBN | : 0898717574 |
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
Author | : Per Christian Hansen |
Publisher | : SIAM |
Total Pages | : 219 |
Release | : 2010-03-18 |
Genre | : Mathematics |
ISBN | : 0898716969 |
An introduction to the practical treatment of inverse problems using numerical methods for graduate students, including examples and exercises.
Author | : Richard C. Aster |
Publisher | : Elsevier |
Total Pages | : 406 |
Release | : 2018-10-16 |
Genre | : Science |
ISBN | : 0128134232 |
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 | : Mikhail M. Lavrent'ev |
Publisher | : Walter de Gruyter |
Total Pages | : 288 |
Release | : 2012-05-07 |
Genre | : Mathematics |
ISBN | : 3110915529 |
This monograph deals with the theory of inverse problems of mathematical physics and applications of such problems. Besides it considers applications and numerical methods of solving the problems under study. Descriptions of particular numerical experiments are also included.
Author | : Martin Hanke |
Publisher | : SIAM |
Total Pages | : 171 |
Release | : 2017-01-01 |
Genre | : Mathematics |
ISBN | : 1611974941 |
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. This book 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. A Taste of Inverse Problems: Basic Theory and Examples 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.
Author | : Yanfei Wang |
Publisher | : Walter de Gruyter |
Total Pages | : 552 |
Release | : 2012-10-30 |
Genre | : Mathematics |
ISBN | : 3110259052 |
Nowadays inverse problems and applications in science and engineering represent an extremely active research field. The subjects are related to mathematics, physics, geophysics, geochemistry, oceanography, geography and remote sensing, astronomy, biomedicine, and other areas of applications. This monograph reports recent advances of inversion theory and recent developments with practical applications in frontiers of sciences, especially inverse design and novel computational methods for inverse problems. The practical applications include inverse scattering, chemistry, molecular spectra data processing, quantitative remote sensing inversion, seismic imaging, oceanography, and astronomical imaging. The book serves as a reference book and readers who do research in applied mathematics, engineering, geophysics, biomedicine, image processing, remote sensing, and environmental science will benefit from the contents since the book incorporates a background of using statistical and non-statistical methods, e.g., regularization and optimization techniques for solving practical inverse problems.
Author | : Adrian Doicu |
Publisher | : Springer Science & Business Media |
Total Pages | : 432 |
Release | : 2010-07-16 |
Genre | : Science |
ISBN | : 3642054390 |
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.
Author | : Jennifer L. Mueller |
Publisher | : SIAM |
Total Pages | : 349 |
Release | : 2012-11-30 |
Genre | : Mathematics |
ISBN | : 1611972345 |
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.
Author | : Charles W. Groetsch |
Publisher | : Springer Science & Business Media |
Total Pages | : 159 |
Release | : 2013-12-14 |
Genre | : Technology & Engineering |
ISBN | : 3322992020 |
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.