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Optimization and Regularization for Computational Inverse Problems and Applications

  • Book
  • © 2011

Overview

Editors:
  1. Yanfei Wang

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

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  2. Changchun Yang

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

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  3. Anatoly G. Yagola

    1. Department of Mathematics Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia

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  • First book relating the inversion theory and recent developments with real applications
  • Combines optimization and regularization for solving inverse problems
  • Covers frontiers on multi-disciplinary subjects areas

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Table of contents (14 chapters)

  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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Keywords

About this book

"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.

Editors and Affiliations

  • 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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