## Optimization and Regularization for Computational Inverse Problems and ApplicationsYanfei Wang, Anatoly G. Yagola, Changchun Yang "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

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 |

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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Optimization and Regularization for Computational Inverse Problems and ... Yanfei Wang,Anatoly G. Yagola,Changchun Yang No preview available - 2011 |

### Common terms and phrases

A. N. Tikhonov algorithm applied approximate solution assume assumption boundary BRDF calculated choice coefficient Computational condition conjugate gradient methods consider constant constraints construct convex defined denote discrepancy principle error estimate exact solution example experimental data extrapolated far-field pattern Fejér force field formula given global convergence gravitational lens Hilbert space ill-posed problems image restoration indicator function inequality integral equation Inverse Problems iterative method iterative processes kernel L-BFGS L-BFGS method Lemma line search linear mapping Math mathematical matrix minimization molecular molecule obstacle obtained operator equation optimization Potthast priori information properties pseudosolution quadratic quasar reconstruction regularization method regularization parameter regularizing algorithm remote sensing right-hand side satisfies scheme sequence smoothness step step-length test domains Theorem Tikhonov regularization trust region unknown vector vibrational wave Wolfe conditions Wolfe line search Y. F. Wang Yuan