Fast Linearized Augmented Lagrangian Method for Euler’s Elastica Model  

作　　者：Jun Zhang Rongliang Chen Chengzhi Deng Shengqian Wang 

机构地区：[1]Jiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing,Nanchang Institute of Technology,Nanchang 330099,Jiangxi,China [2]College of Science,Nanchang Institute of Technology,Nanchang 330099,Jiangxi,China [3]Shenzhen Institutes of Advanced Technology,Chinese Academy of Sciences,Shenzhen 518055,P.R.China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2017年第1期98-115,共18页高等学校计算数学学报（英文版）

基　　金：supported by the NNSF of China grants 11526110,11271069,61362036 and 61461032,the 863 Program of China grant 2015AA01A302;the Open Research Fund of Jiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing(2016WICSIP013);the Youth Foundation of Nanchang Institute of Technology(2014KJ021).

摘　　要：Recently,many variational models involving high order derivatives have been widely used in image processing,because they can reduce staircase effects during noise elimination.However,it is very challenging to construct efficient algo-rithms to obtain the minimizers of original high order functionals.In this paper,we propose a new linearized augmented Lagrangian method for Euler’s elastica image denoising model.We detail the procedures of finding the saddle-points of the aug-mented Lagrangian functional.Instead of solving associated linear systems by FFTor linear iterative methods(e.g.,the Gauss-Seidel method),we adopt a linearized strat-egy to get an iteration sequence so as to reduce computational cost.In addition,we give some simple complexity analysis for the proposed method.Experimental results with comparison to the previous method are supplied to demonstrate the efficiency of the proposed method,and indicate that such a linearized augmented Lagrangian method is more suitable to deal with large-sized images.

关 键 词：Image denoising Euler’s elastica model linearized augmented Lagrangian method shrink operator closed form solution 

分 类 号：O17[理学—数学]