Optimization and Regularization for Computational Inverse Problems and Applications

1. Front Matter

   Pages i-xvii

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2. Introduction

   1. Front Matter

      Pages 1-1

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   2. Inverse Problems, Optimization and Regularization: A Multi-Disciplinary Subject

      • Yanfei Wang, Changchun Yang

      Pages 3-14

3. Regularization Theory and Recent Developments

   1. Front Matter

      Pages 15-15

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   2. Ill-Posed Problems and Methods for Their Numerical Solution

      • Anatoly G. Yagola

      Pages 17-34

   3. Inverse Problems with A Priori Information

      • Vladimir V. Vasin

      Pages 35-64

   4. Regularization of Naturally Linearized Parameter Identification Problems and the Application of the Balancing Principle

      • Hui Cao, Sergei Pereverzyev

      Pages 65-105

   5. Extrapolation Techniques of Tikhonov Regularization

      • Tingyan Xiao, Yuan Zhao, Guozhong Su

      Pages 107-126

   6. Modified Regularization Scheme with Application in Reconstructing Neumann-Dirichlet Mapping

      • Pingli Xie, Jin Cheng

      Pages 127-138

4. Nonstandard Regularization and Advanced Optimization Theory and Methods

   1. Front Matter

      Pages 139-139

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   2. Gradient Methods for Large Scale Convex Quadratic Functions

      • Yaxiang Yuan

      Pages 141-155

   3. Convergence Analysis of Nonlinear Conjugate Gradient Methods

      • Yuhong Dai

      Pages 157-181

   4. Full Space and Subspace Methods for Large Scale Image Restoration

      • Yanfei Wang, Shiqian Ma, Qinghua Ma

      Pages 183-201

5. Numerical Inversion in Geoscience and Quantitative Remote Sensing

   1. Front Matter

      Pages 203-203

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   2. Some Reconstruction Methods for Inverse Scattering Problems

      • Jijun Liu, Haibing Wang

      Pages 205-247

   3. Inverse Problems of Molecular Spectra Data Processing

      • Gulnara Kuramshina

      Pages 249-272

   4. Numerical Inversion Methods in Geoscience and Quantitative Remote Sensing

      • Yanfei Wang, Xiaowen Li

      Pages 273-299

   5. Pseudo-Differential Operator and Inverse Scattering of Multidimensional Wave Equation

      • Hong Liu, Li He

      Pages 301-325

   6. Tikhonov Regularization for Gravitational Lensing Research

      • Boris Artamonov, Ekaterina Koptelova, Elena Shimanovskaya, Anatoly G. Yagola

      Pages 327-347

6. Back Matter

   Pages 349-350

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"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.

• Geosciences
• HEP
• Inverse Problems
• Numerical Inversion
• Optimization
• Regularization Theory
• Signal/Image/Data Processing
• remote sensing/photogrammetry

• Key Laboratory of Petroleum Geophysics Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China

  Yanfei Wang, Changchun Yang

• Department of Mathematics Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia

  Anatoly G. Yagola

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