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Preconditioned Iterative Methods for Algebraic Systems from Multiplicative Half-Quadratic Regularization Image Restorations
作者姓名:Zhong-Zhi  Yu-Mei  K.
作者单位:[1]State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719,Beijing 100190, China [2]School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000,Gansu, China [3]Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
基金项目:the National Basic Research Program,the National Outstanding Young Scientist Foundation,the Specialized Research Grant for High Educational Doctoral Program,Hong Kong RGC grants and HKBU FRGs
摘    要:<正>Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term.A regularized convex term can usually preserve the image edges well in the restored image.In this paper,we consider a class of convex and edge-preserving regularization functions,i.e.,multiplicative half-quadratic regularizations,and we use the Newton method to solve the correspondingly reduced systems of nonlinear equations.At each Newton iterate,the preconditioned conjugate gradient method,incorporated with a constraint preconditioner,is employed to solve the structured Newton equation that has a symmetric positive definite coefficient matrix. The eigenvalue bounds of the preconditioned matrix are deliberately derived,which can be used to estimate the convergence speed of the preconditioned conjugate gradient method.We use experimental results to demonstrate that this new approach is efficient, and the effect of image restoration is reasonably well.

关 键 词:Image  conjugate  gradient  method  image  restoration  symmetric  positive  definite  energy  function  Newton  method  matrix  approach  results  use  paper  class  new

Preconditioned Iterative Methods for Algebraic Systems from Multiplicative Half-Quadratic Regularization Image Restorations
Zhong-Zhi,Yu-Mei,K..Preconditioned Iterative Methods for Algebraic Systems from Multiplicative Half-Quadratic Regularization Image Restorations[J].Numerical Mathematics A Journal of Chinese Universities English Series,2010,3(4).
Authors:Zhong-Zhi Bai  Yu-Mei Huang  Michael K Ng  Xi Yang
Abstract:Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term. A regularized convex term can usually preserve the image edges well in the restored image. In this paper, we consider a class of convex and edge-preserving regularization functions, I.e., multiplicative half-quadratic regularizations, and we use the Newton method to solve the correspondingly reduced systems of nonlinear equations. At each Newton iterate, the preconditioned conjugate gradient method, incorporated with a constraint preconditioner, is employed to solve the structured Newton equation that has a symmetric positive definite coefficient matrix.The igenvalue bounds of the preconditioned matrix are deliberately derived, which can be used to estimate the convergence speed of the preconditioned conjugate gradient method. We use experimental results to demonstrate that this new approach is efficient,and the effect of image restoration is r0easonably well.
Keywords:Edge-preserving  image restoration  multiplicative half-quadratic regularization  Newton method  preconditioned conjugate gradient method  constraint preconditioner  eigenvalue bounds
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