Optimization and Regularization for Computational Inverse Problems and Applications

Part I. Introduction

1. Inverse Problems, Optimization and Regularization: A Multi-Disciplinary Subject
Yanfei Wang, Changchun Yang

Part II. Regularization Theory and Recent Developments

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

3. Inverse Problems with A Priori Information
Vladimir V. Vasin

4. Regularization of Naturally Linearized Parameter Identification Problems and the Application of the Balancing Principle
Hui Cao, Sergei Pereverzyev

5. Extrapolation Techniques of Tikhonov Regularization
Tingyan Xiao, Yuan Zhao, Guozhong Su

6. Modified Regularization Scheme with Application in Reconstructing Neumann-Dirichlet Mapping
Pingli Xie, Jin Cheng

Part III. Nonstandard Regularization and Advanced Optimization Theory and Methods

7. Gradient Methods for Large Scale Convex Quadratic Functions
Yaxiang Yuan

8. Convergence Analysis of Nonlinear Conjugate Gradient Methods
Yuhong Dai

9. Full Space and Subspace Methods for Large Scale Image Restoration
Yanfei Wang, Shiqian Ma, Qinghua Ma

Part IV. Numerical Inversion in Geoscience and Quantitative Remote Sensing

10. Some Reconstruction Methods for Inverse Scattering Problems
Jijun Liu, Haibing Wang

11. Inverse Problems of Molecular Spectra Data Processing
Gulnara Kuramshina

12. Numerical Inversion Methods in Geoscience and Quantitative Remote Sensing
Yanfei Wang, Xiaowen Li

13. Pseudo-Differential Operator and Inverse Scattering of Multidimensional Wave Equation
Hong Liu, Li He

14. Tikhonov Regularization for Gravitational Lensing Research
Boris Artamonov, Ekaterina Koptelova, Elena Shimanovskaya, Anatoly G. Yagola

Keywords: Mathematics, Computational Mathematics and Numerical Analysis, Appl.Mathematics/Computational Methods of Engineering, Remote Sensing/Photogrammetry