Singular Regularization Of Inverse Problems

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Singular Regularization Of Inverse Problems

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Author : Martin Benning
language : en
Publisher:
Release Date : 2011

Singular Regularization Of Inverse Problems written by Martin Benning and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.

Large Scale Inverse Problems

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Author : Mike Cullen
language : en
Publisher: Walter de Gruyter
Release Date : 2013-08-29

Large Scale Inverse Problems written by Mike Cullen and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-29 with Mathematics categories.

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.

Parameter Estimation And Inverse Problems

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Author : Richard C. Aster
language : en
Publisher: Academic Press
Release Date : 2013

Parameter Estimation And Inverse Problems written by Richard C. Aster and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.

Preface -- 1. Introduction -- 2. Linear Regression -- 3. Discretizing Continuous Inverse Problems -- 4. Rank Deficiency and Ill-Conditioning -- 5. Tikhonov Regularization -- 6. Iterative Methods -- 7. Other Regularization Techniques -- 8. Fourier Techniques -- 9. Nonlinear Regression -- 10. Nonlinear Inverse Problems -- 11. Bayesian Methods -- Appendix A: Review of Linear Algebra -- Appendix B: Review of Probability and Statistics -- Appendix C: Glossary of Notation -- Bibliography -- IndexLinear Regression -- Discretizing Continuous Inverse Problems -- Rank Deficiency and Ill-Conditioning -- Tikhonov Regularization -- Iterative Methods -- Other Regularization Techniques -- Fourier Techniques -- Nonlinear Regression -- Nonlinear Inverse Problems -- Bayesian Methods.

Inverse Problems Design And Optimization Vol 1

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Author :
language : en
Publisher: Editora E-papers
Release Date :

Inverse Problems Design And Optimization Vol 1 written by and has been published by Editora E-papers this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Inverse Problems And Optimal Design In Electricity And Magnetism

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Author : Pekka Neittaanmäki
language : en
Publisher: Oxford University Press
Release Date : 1996-01-11

Inverse Problems And Optimal Design In Electricity And Magnetism written by Pekka Neittaanmäki and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-11 with Language Arts & Disciplines categories.

The impact of optimization methods in electromagnetism has been much less than in mechanical engineering and particularly the solution of inverse problems in structural mechanics. This book addresses this omission: it will serve as a guide to the theory as well as the computer implementation of solutions. It is self-contained covering all the mathematical theory necessary.

Solving The Inverse Problem Of Electrocardiography In A Realistic Environment

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Author : Yuan Jiang
language : en
Publisher: KIT Scientific Publishing
Release Date : 2014-08-13

Solving The Inverse Problem Of Electrocardiography In A Realistic Environment written by Yuan Jiang and has been published by KIT Scientific Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-13 with Technology & Engineering categories.

Heart disease is a leading cause of death worldwide. Straightforward information about the cardiac electrophysiology can help to improve the quality of diagnosis of heart diseases. The inverse problem of electrocardiography and the intracardiac catheter measurement are two ways to get access to the electrophysiology in the heart. In this thesis six research topics related to these two techniques are included.

Inverse Problems And Imaging

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Author : Ana Carpio
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-17

Inverse Problems And Imaging written by Ana Carpio 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 2008-04-17 with Mathematics categories.

In the CIME Summer School on Imaging, experts in mathematical techniques and applications presented useful introductions to many aspects of the field. This volume contains updated lectures as well as additional contributions on other related topics.

Optimization And Regularization For Computational Inverse Problems And Applications

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Author : Yanfei Wang
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-29

Optimization And Regularization For Computational Inverse Problems And Applications written by Yanfei Wang 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 2011-06-29 with Mathematics categories.

"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.

Experimental And Numerical Methods For Solving Ill Posed Inverse Problems

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Author : Randall L. Barbour
language : en
Publisher: SPIE-International Society for Optical Engineering
Release Date : 1995

Experimental And Numerical Methods For Solving Ill Posed Inverse Problems written by Randall L. Barbour and has been published by SPIE-International Society for Optical Engineering this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Computers categories.

Mathematical And Numerical Approaches For Multi Wave Inverse Problems

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Author : Larisa Beilina
language : en
Publisher: Springer Nature
Release Date : 2020-06-30

Mathematical And Numerical Approaches For Multi Wave Inverse Problems written by Larisa Beilina and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-30 with Mathematics categories.

This proceedings volume gathers peer-reviewed, selected papers presented at the “Mathematical and Numerical Approaches for Multi-Wave Inverse Problems” conference at the Centre Internacional de Rencontres Mathématiques (CIRM) in Marseille, France, in April 2019. It brings the latest research into new, reliable theoretical approaches and numerical techniques for solving nonlinear and inverse problems arising in multi-wave and hybrid systems. Multi-wave inverse problems have a wide range of applications in acoustics, electromagnetics, optics, medical imaging, and geophysics, to name but a few. In turn, it is well known that inverse problems are both nonlinear and ill-posed: two factors that pose major challenges for the development of new numerical methods for solving these problems, which are discussed in detail. These papers will be of interest to all researchers and graduate students working in the fields of nonlinear and inverse problems and its applications.