Linear Inverse Problems And Tikhonov Regularization
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Linear Inverse Problems And Tikhonov Regularization
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Author : Mark S. Gockenbach
language : en
Publisher:
Release Date : 2016
Linear Inverse Problems And Tikhonov Regularization written by Mark S. Gockenbach and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Linear Inverse Problems And Tikhonov Regularization
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Author : Mark S. Gockenbach
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-12-31
Linear Inverse Problems And Tikhonov Regularization written by Mark S. Gockenbach and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-31 with Mathematics categories.
Inverse problems occur frequently in science and technology, whenever we need to infer causes from effects that we can measure. Mathematically, they are difficult problems because they are unstable: small bits of noise in the measurement can completely throw off the solution. Nevertheless, there are methods for finding good approximate solutions. Linear Inverse Problems and Tikhonov Regularization examines one such method: Tikhonov regularization for linear inverse problems defined on Hilbert spaces. This is a clear example of the power of applying deep mathematical theory to solve practical problems. Beginning with a basic analysis of Tikhonov regularization, this book introduces the singular value expansion for compact operators, and uses it to explain why and how the method works. Tikhonov regularization with seminorms is also analyzed, which requires introducing densely defined unbounded operators and their basic properties. Some of the relevant background is included in appendices, making the book accessible to a wide range of readers.
Inverse Problems Tikhonov Theory And Algorithms
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Author : Ito Kazufumi
language : en
Publisher: World Scientific
Release Date : 2014-08-28
Inverse Problems Tikhonov Theory And Algorithms written by Ito Kazufumi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-28 with Mathematics categories.
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.
Regularization Of Inverse Problems
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Author : Heinz Werner Engl
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-03-31
Regularization Of Inverse Problems written by Heinz Werner Engl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-31 with Mathematics categories.
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.
Inverse Problems
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Author : Mathias Richter
language : en
Publisher: Springer Nature
Release Date : 2021-01-05
Inverse Problems written by Mathias Richter and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-05 with Mathematics categories.
This textbook is an introduction to the subject of inverse problems with an emphasis on practical solution methods and applications from geophysics. The treatment is mathematically rigorous, relying on calculus and linear algebra only; familiarity with more advanced mathematical theories like functional analysis is not required. Containing up-to-date methods, this book will provide readers with the tools necessary to compute regularized solutions of inverse problems. A variety of practical examples from geophysics are used to motivate the presentation of abstract mathematical ideas, thus assuring an accessible approach. Beginning with four examples of inverse problems, the opening chapter establishes core concepts, such as formalizing these problems as equations in vector spaces and addressing the key issue of ill-posedness. Chapter Two then moves on to the discretization of inverse problems, which is a prerequisite for solving them on computers. Readers will be well-prepared for the final chapters that present regularized solutions of inverse problems in finite-dimensional spaces, with Chapter Three covering linear problems and Chapter Four studying nonlinear problems. Model problems reflecting scenarios of practical interest in the geosciences, such as inverse gravimetry and full waveform inversion, are fully worked out throughout the book. They are used as test cases to illustrate all single steps of solving inverse problems, up to numerical computations. Five appendices include the mathematical foundations needed to fully understand the material. This second edition expands upon the first, particularly regarding its up-to-date treatment of nonlinear problems. Following the author’s approach, readers will understand the relevant theory and methodology needed to pursue more complex applications. Inverse Problems is ideal for graduate students and researchers interested in geophysics and geosciences.
Discrete Inverse Problems
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Author : Per Christian Hansen
language : en
Publisher: SIAM
Release Date : 2010-01-01
Discrete Inverse Problems written by Per Christian Hansen and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-01 with Mathematics categories.
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.
Inverse Problems
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Author : Kazufumi Ito
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2014-07
Inverse Problems written by Kazufumi Ito and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07 with Mathematics categories.
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.
Variational Source Conditions Quadratic Inverse Problems Sparsity Promoting Regularization
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Author : Jens Flemming
language : en
Publisher: Springer
Release Date : 2018-09-08
Variational Source Conditions Quadratic Inverse Problems Sparsity Promoting Regularization written by Jens Flemming and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-08 with Mathematics categories.
The book collects and contributes new results on the theory and practice of ill-posed inverse problems. Different notions of ill-posedness in Banach spaces for linear and nonlinear inverse problems are discussed not only in standard settings but also in situations up to now not covered by the literature. Especially, ill-posedness of linear operators with uncomplemented null spaces is examined.Tools for convergence rate analysis of regularization methods are extended to a wider field of applicability. It is shown that the tool known as variational source condition always yields convergence rate results. A theory for nonlinear inverse problems with quadratic structure is developed as well as corresponding regularization methods. The new methods are applied to a difficult inverse problem from laser optics.Sparsity promoting regularization is examined in detail from a Banach space point of view. Extensive convergence analysis reveals new insights into the behavior of Tikhonov-type regularization with sparsity enforcing penalty.
Variational Regularization For Systems Of Inverse Problems
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Author : Richard Huber
language : en
Publisher: Springer
Release Date : 2019-02-14
Variational Regularization For Systems Of Inverse Problems written by Richard Huber and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-14 with Mathematics categories.
Tikhonov regularization is a cornerstone technique in solving inverse problems with applications in countless scientific fields. Richard Huber discusses a multi-parameter Tikhonov approach for systems of inverse problems in order to take advantage of their specific structure. Such an approach allows to choose the regularization weights of each subproblem individually with respect to the corresponding noise levels and degrees of ill-posedness.
Regularization For Applied Inverse And Ill Posed Problems
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Author :
language : de
Publisher: Springer-Verlag
Release Date : 2013-11-22
Regularization For Applied Inverse And Ill Posed Problems written by and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-22 with Technology & Engineering categories.