（计算反演问题中的优化与正则化方法及其应用）(国内英文版)Optimization and Regularization for Computational Inverse Problems and Applicationspdf/txt下载_在线阅读全文

（计算反演问题中的优化与正则化方法及其应用）(国内英文版)Optimization and Regularization for Computational Inverse Problems and Applications

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版次：1
页数：
字数：
印刷时间：2010年05月01日
开本：16开
纸张：胶版纸
包装：精装
是否套装：否
国际标准书号ISBN：9787040285154

作者:王彦飞，（俄）亚哥拉，杨长春　主编出版社:高等教育出版社出版时间:2010年05月

内容简介

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.

目　　录

Part I Introduction
1 Inverse Problems, Optimization and Regularization: A
Multi-Disciplinary Subject
Yanfei Wang and Changchun Yang
1.1 Introduction
1.2 Examples about mathematical inverse problems
1.3 Examples in applied science and engineering
1.4 Basic theory
1.5 Scientific computing
1.6 Conclusion
Referertces
Part II Regularization Theory and Recent Developments
2 Ill-Posed Problems and Methods for Their Numerical Solution
Anatoly G. Yagola

Part I Introduction 1 Inverse Problems, Optimization and Regularization: A Multi-Disciplinary Subject Yanfei Wang and Changchun Yang 1.1 Introduction 1.2 Examples about mathematical inverse problems 1.3 Examples in applied science and engineering 1.4 Basic theory 1.5 Scientific computing 1.6 Conclusion Referertces Part II Regularization Theory and Recent Developments 2 Ill-Posed Problems and Methods for Their Numerical Solution Anatoly G. Yagola 2.1 Well-posed and ill-posed problems 2.2 Definition of the regularizing algorithm 2.3 Ill-posed problems on compact sets 2.4 Ill-posed problems with sourcewise represented solutions 2.5 Variational approach for constructing regularizing algorithms 2.6 Nonlinear ill-posed problems 2.7 Iterative and other methods References 3 Inverse Problems with A Priori Information Vladimir V. Vasin 3.1 Introduction 3.2 Formulation of the problem with a priori information 3.3 The main classes of mappings of the Fejer type and their properties 3.4 Convergence theorems of the method of successive approximations for the pseudo-contractive operators 3.5 Examples of operators of the Fejer type 3.6 Fejer processes for nonlinear equations 3.7 Applied problems with a priori information and methods for solution 3.7.1 Atomic structure characterization 3.7.2 Radiolocation of the ionosphere 3.7.3 Image reconstruction 3.7.4 Thermal sounding of the atmosphere 3.7.5 Testing a wellbore/reservoir 3.8 Conclusions References 4 Regularization of Naturally Linearized Parameter Identification Problems and the Application of the Balancing Principle Hui Cao and Sergei Pereverzyev 4.1 Introduction 4.2 Discretized Tikhonov regularization and estimation of accuracy 4.2.1 Generalized source condition 4.2.2 Discretized Tikhonov regularization 4.2.3 Operator monotone index functions 4.2.4 Estimation of the accuracy 4.3 Parameter identification in elliptic equation 4.3.1 Natural linearization 4.3.2 Data smoothing and noise level analysis 4.3.3 Estimation of the accuracy 4.3.4 Balancing principle 4.3.5 Numerical examples 4.4 Parameter identification in parabolic equation 4.4.1 Natural linearization for recovering b(x) = a(u(T, x)) 4.4.2 Regularized identification of the diffusion coefficient a(u) 4.4.3 Extended balancing principle 4.4.4 Numerical examples References 5 Extrapolation Techniques of Tikhonov Regularization Tingyan Xiao, Yuan Zhao and Guozhong Su 5.1 Introduction 5.2 Notations and preliminaries 5.3 Extrapolated regularization based on vector-valued function approximation 5.3.1 Extrapolated scheme based on Lagrange interpolation 5.3.2 Extrapolated scheme based on Hermitian interpolation 5.3.3 Extrapolation scheme based on rational interpolation 5.4 Extrapolated regularization based on improvement of regularizing qualification 5.5 The choice of parameters in the extrapolated regularizing approximation 5.6 Numerical experiments 5.7 Conclusion References 6 Modified Regularization Scheme with Application in Reconstructing Neumann-Dirichlet Mapping Pingli Xie and Jin Cheng 6.1 Introduction 6.2 Regularization method 6.3 Computational aspect 6.4 Numerical simulation results for the modified regularization 6.5 The Neumann-Dirichlet mapping for elliptic equation of second order 6.6 The numerical results of the Neumann-Dirichlet mapping 6.7 Conclusion References Part III Nonstandard Regularization and Advanced Optimization Theory and Methods 7 Gradient Methods for Large Scale Convex Quadratic Functions Yaxiang Yuan 7.1 Introduction 7.2 A generalized convergence result 7.3 Short BB steps 7.4 Numerical results 7.5 Discussion and conclusion References 8 Convergence Analysis of Nonlinear Conjugate Gradient Methods Yuhong Dai 8.1 Introduction 8.2 Some preliminaries 8.3 A sufficient and necessary condition on βk 8.3.1 Proposition of the condition 8.3.2 Sufficiency of (8.3.5) 8.3.3 Necessity of (8.3.5) 8.4 Applications of the condition (8.3.5) 8.4.1 Property (#) 8.4.2 Applications to some known conjugate gradient methods 8.4.3 Application to a new conjugate gradient method 8.5 Discussion References 9 Full Space and Subspace Methods for Large Scale Image Restoration Yanfei Wang, Shiqian Ma and Qinghua Ma 9.1 Introduction 9.2 Image restoration without regularization 9.3 Image restoration with regularization 9.4 Optimization methods for solving the smoothing regularized functional 9.4.1 Minimization of the convex quadratic programming problem with projection 9.4.2 Limited memory BFGS method with projection 9.4.3 Subspace trust region methods 9.5 Matrix-Vector Multiplication (MVM) 9.5.1 MVM: FFT-based method 9.5.2 MVM with sparse matrix 9.6 Numerical experiments 9.7 Conclusions References Part IV Numerical Inversion in Geoscience and Quantitative Remote Sensing 10 Some Reconstruction Methods for Inverse Scattering Problems Jijun Liu and Haibing Wang 10.1 Introduction 10.2 Iterative methods and decomposition methods 10.2.1 Iterative methods 10.2.2 Decomposition methods 10.2.3 Hybrid method 10.3 Singular source methods 10.3.1 Probe method 10.3.2 Singular sources method 10.3.3 Linear sampling method 10.3.4 Factorization method 10.3.5 Range test method 10.3.6 No response test method 10.4 Numerical schemes References 11 Inverse Problems of Molecular Spectra Data Processing Gulnara Kuramshina 11.1 Introduction 11.2 Inverse vibrational problem 11.3 The mathematical formulation of the inverse vibrational problem 11.4 Regularizing algorithms for solving the inverse vibrational problem 11.5 Model of scaled molecular force field 11.6 General inverse problem of structural chemistry 11.7 Intermolecular potential 11.8 Examples of calculations 11.8.1 Calculation of methane intermolecular potential 11.8.2 Prediction of vibrational spectrum of fullerene C240 References 12 Numerical Inversion Methods in Geoscience and Quantitative Remote Sensing Yanfei Wang and Xiaowen Li 12.1 Introduction 12.2 Examples of quantitative remote sensing inverse problems: land surface parameter retrieval problem 12.3 Formulation of the forward and inverse problem 12.4 What causes ill-posedness 12.5 Tikhonov variational regularization 12.5.1 Choices of the scale operator D 12.5.2 Regularization parameter selection methods 12.6 Solution methods 12.6.1 Gradient-type methods 12.6.2 Newton-type methods 12.7 Numerical examples 12.8 Conclusions References 13 Pseudo-Differential Operator and Inverse Scattering of Multidimensional Wave Equation Hong Liu, Li He 13.1 Introduction 13.2 Notations of operators and symbols 13.3 Description in symbol domain 13.4 Lie algebra integral expressions 13.5 Wave equation on the ray coordinates 13.6 Symbol expression of one-way wave operator equations 13.7 Lie algebra expression of travel time 13.8 Lie algebra integral expression of prediction operator 13.9 Spectral factorization expressions of reflection data 13.10 Conclusions References 14 Tikhonov Regularization for Gravitational Lensing Research. Boris Artamonov, Ekaterina Koptelova, Elena Shimanovskaya and Anatoly G. Yagola 14.1 Introduction 14.2 Regularized deconvolution of images with point sources and smooth background 14.2.1 Formulation of the problem 14.2.2 Tikhonov regularization approach 14.2.3 A priori information 14.3 Application of the Tikhonov regularization approach to quasar profile reconstruction 14.3.1 Brief introduction to microlensing 14.3.2 Formulation of the problem 14.3.3 Implementation of the Tikhonov regularization approach 14.3.4 Numerical results of the Q2237 profile reconstruction 14.4 Conclusions References Index

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