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Iterative implementation of the adaptive regularization yields optimality

science china mathematics 2005年第4期48卷 485-492页

作者： ma qinghua & wang yanfei department of information sciences, college of arts and science of beijing union university, beijing 10003., china National Key Laboratory on Remote Sensing science, Institute of Remote Sensing Applications, Chinese Academy of sciences, beijing 100101, china department of mathematics, university of Central Florida, P. O. Box 161364, Orlando, FL 32816-1364, USA 1. department of information sciences College of Arts and Science of Beijing Union University 100038 Beijing China 2. National Key Laboratory on Remote Sensing science Institute of Remote Sensing Applications Chinese Academy of Sciences 100101 Beijing China

The adaptive regularization method is first proposed by Ryzhikov et al. for the deconvolution in elimination of multiples. This method is stronger than the Tikhonov regularization in the sense that itis adaptive, i.e. it eliminates the small eigenvalues of theadjoint operator when it is nearly singular. We will show in this paper that the adaptive regularization can be implemented iterately. Some properties of the proposed non-stationary iterated adaptive regularization method are analyzed. The rate of convergence for inexact data is proved. Therefore the iterative implementation of the adaptive regularization can yield optimality.

关键词： ill-posed problems, non-stationary iterated adaptive regularization, optimality.

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Chapter 9 Full Space and Subspace Methods for Large Scale Image Restoration

Chapter 9 Full Space and Subspace Methods for Large Scale Im...

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中国科学院地质与地球物理研究所第十届(2010年度)学术年会

作者： yanfei wang Institute of Geology and Geophysics,Chinese Academy of sciences,beijing 100029,china. Shiqian ma department of Industrial Engineering and Operations Research,Columbia university, New York,NY 10027-6902,USA. qinghua ma~(1,2) 1 School of information,Renmin university of china,beijing,100872,china. 2 college of Art and science,beijing union university,beijing,100083,china.

In this chapter,we discuss about the full space and subspace methods for ill-posed image restoration *** restoration refers to minimizing the degradation which is caused by sensing environment,say CCD camera misfocus, nonuniform motion,atmospheric aerosols and atmospheric *** image restoration problems,a key matter is to solve a quadratic programming *** study numerical solution methods in full space by limited memory of BFGS method and the subspace trust region *** develop a novel approach for reducing the cost of sparse matrix-vector multiplication when applying the full space and subspace methods to atmospheric image *** the projection technique for the regularized convex quadratic functional is developed in the iteration for ensuring *** experiments indicate that these methods are useful for large-scale image restoration problems.

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