Optimization and Regularization for Computational Inverse Problems and Applications

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Yanfei Wang, Anatoly G. Yagola, Changchun Yang
Springer Science & Business Media, Jun 29, 2011 - Mathematics - 400 pages
"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.
 

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Contents

A MultiDisciplinary Subject
3
Part II Regularization Theory and Recent Developments
15
Chapter 2 IllPosed Problems and Methods for Their Numerical Solution
17
Chapter 3 Inverse Problems with A Priori Information
35
Chapter 4 Regularization of Naturally Linearized Parameter Identification Problems and the Application of the Balancing Principle
65
Chapter 5 Extrapolation Techniques of Tikhonov Regularization
106
Chapter 6 Modified Regularization Scheme with Application in Reconstructing NeumannDirichlet Mapping
127
Part III Nonstandard Regularization and Advanced Optimization Theory and Methods
139
Chapter 9 Full Space and Subspace Methods for Large Scale Image Restoration
183
Part IV Numerical Inversion in Geoscience and Quantitative Remote Sensing
202
Chapter 10 Some Reconstruction Methods for Inverse Scattering Problems
205
Chapter 11 Inverse Problems of Molecular Spectra Data Processing
248
Chapter 12 Numerical Inversion Methods in Geoscience and Quantitative Remote Sensing
273
Chapter 13 PseudoDifferential Operator and Inverse Scattering of Multidimensional Wave Equation
301
Chapter 14 Tikhonov Regularization for Gravitational Lensing Research
326
Index
348

Chapter 7 Gradient Methods for Large Scale Convex Quadratic Functions
141
Chapter 8 Convergence Analysis of Nonlinear Conjugate Gradient Methods
156

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