Preconditioning techniques for an image deblurring problem

被引：9
|
作者：
Chen, Ke [1 ]
Fairag, Faisal [2 ]
Al-Mahdi, Adel [2 ]
机构：
[1] Univ Liverpool, Dept Math Sci, Liverpool L69 7ZL, Merseyside, England
[2] KFUPM, Dept Math & Stat, Dhahran 31261, Saudi Arabia
来源：
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS | 2016年 / 23卷 / 03期
基金：
英国工程与自然科学研究理事会;
关键词：
preconditioning technique; saddle-point problems; image deblurring; Krylov subspace method; TV regularization; primal dual formulation; BTTB matrix; FFT; BLOCK TOEPLITZ-SYSTEMS; RESTORATION; MATRICES;
D O I：
10.1002/nla.2040
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the solution of a large linear system of equations, which is obtained from discretizing the Euler-Lagrange equations associated with the image deblurring problem. The coefficient matrix of this system is of the generalized saddle point form with high condition number. One of the blocks of this matrix has the block Toeplitz with Toeplitz block structure. This system can be efficiently solved using the minimal residual iteration method with preconditioners based on the fast Fourier transform. Eigenvalue bounds for the preconditioner matrix are obtained. Numerical results are presented. Copyright (C) 2016 John Wiley & Sons, Ltd.
引用
收藏
页码：570 / 584
页数：15
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