计算数学
       首页 |  期刊介绍 |  编委会 |  投稿指南 |  期刊订阅 |  下载中心 |  留言板 |  联系我们 |  在线办公 | 
计算数学  2018, Vol. 40 Issue (1): 85-95    DOI:
论文 最新目录 | 下期目录 | 过刊浏览 | 高级检索 Previous Articles  |  Next Articles  
一种基于邻近点算法的变步长原始-对偶算法
申远1, 李倩倩1, 吴坚2
1. 南京财经大学应用数学学院, 南京 210023;
2. 哈尔滨工业大学深圳研究生院计算机科学与技术学院, 深圳 518000
A VARIABLE STEP-SIZE PRIMAL-DUAL ALGORITHM BASED ON PROXIMAL POINT ALGORITHM
Shen Yuan1, Li Qianqian1, Wu Jian2
1. School of Applied Mathematics, Nanjing University of Financeand Economics, Nanjing 210023, China;
2. School of Computer Science and Technology, Harbin Institute of Technology Shenzhen Graduate School, Shenzhen 518000, China
 全文: PDF (472 KB)   HTML (1 KB)   输出: BibTeX | EndNote (RIS)      背景资料
摘要 本文考虑求解一种源于信号及图像处理问题的鞍点问题.基于邻近点算法的思想,我们对原始-对偶算法进行改进,构造一种对称正定且可变的邻近项矩阵,得到一种新的原始-对偶算法.新算法可以看成一种邻近点算法,因此它的收敛性易于分析,且无需较强的假设条件.初步实验结果表明,当新算法被应用于求解图像去模糊问题时,和其他几种主流的高效算法相比,新算法能得到较高质量的结果,且计算时间也是有竞争力的.
服务
把本文推荐给朋友
加入我的书架
加入引用管理器
E-mail Alert
RSS
作者相关文章
关键词图像去噪   原始-对偶方法   邻近点算法     
Abstract: In this paper, we consider a saddle point problem arising from the applications of signal and image processing. Based on the idea of proximal point algorithm, we improve the primal-dual algorithm by adopting a positive-definite and variate matrix as proximal matrix, and obtain a novel primal-dual algorithm. The new algorithm can be interpreted as a proximal point algorithm, hence the convergence can be derived under mild assumptions. Preliminary experimental results show that when the new algorithm is applied to solve the image denoising problem, compared with some existing efficient algorithms, the new algorithm can obtain a result with higher quality, and the computation time is also competitive.
Key wordsImage denoising   Primal-dual method   Proximal point algorithm   
收稿日期: 2017-03-14;
基金资助:

国家自然科学基金青年项目(11401295);江苏省自然科学基金青年项目(BK20141007);国家社科基金重点项目(12&ZD114);国家社科基金一般项目(15BGL58);江苏省社科基金青年项目(14EUA001)和江苏省青蓝工程项目;国家自然科学基金数学天元基金数学访问学者项目(11726618).

引用本文:   
. 一种基于邻近点算法的变步长原始-对偶算法[J]. 计算数学, 2018, 40(1): 85-95.
. A VARIABLE STEP-SIZE PRIMAL-DUAL ALGORITHM BASED ON PROXIMAL POINT ALGORITHM[J]. Mathematica Numerica Sinica, 2018, 40(1): 85-95.
 
[1] Beck A, Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems[J]. SIAM J Imaging Sci, 2008, 2(1):183-202.
[2] Chambolle A, DeVore R, Lee N, Lucier B. Nonlinear wavelet image processing:Variational problems, compression, and noise removal through wavelet shrinkage[J]. IEEE Trans Imag Proc, 1998, 7:319-335.
[3] Chambolle A, Pock T. A first-order primal-dual algorithms for convex problem with applications to imaging[J]. J Math Imaging Vis 2011, 40(1):120-145.
[4] He B S, Yuan X M. Convergence analysis of primal-dual algorithms for a saddle-point problem:From contraction perspective[J]. SIAM J Imaging Sci, 2012, 5:119-149.
[5] Donoho D. Compressed sensing[J]. IEEE Trans. Inform. Theory, 2006, 52:1289-1306.
[6] Esser E, Zhang X, Chan T F. A general framework for a class of first-order primal-dual algorithms for TV minimization[J]. SIAM J Imaging Sci, 2010, 3:1015-1046.
[7] Yu G H, Qi L Q, Dai Y H. On nonmonotone Chambolle gradient projection algorithms for total variation image restoration[J]. J Math Imaging Vis, 2009, 35:143-154.
[8] Rudin L, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms[J]. Physica D, 1992, 60:259-268.
[9] Figueiredo M, Nowak R. An EM algorithm for wavelet-based image restoration[J]. IEEE Tran Image Process, 2003, 12:906-916.
[10] Zhu M Q, Wright S J, Chan T F. Duality-based algorithms for total variation regularized image restoration[J]. Comput Optim Appl, 2008, 47:377-400.
[11] Zhu M Q, Chan T F. An efficient primal-dual hybrid gradient algorithm for total variation image restoration[R]. UCLA CAM Reports, 2008, 08-34.
[12] Combettes P, Wajs W. Signal recovery by proximal forward-backward splitting[J]. Multiscale Model Sim, 2006, 4(4):1168-1200.
[13] Rockafellar R. Monotone operators and the proximal point algorithm[J]. SIAM J Control Optim, 1976, 14:877-898.
[14] Cai X J, Han D R, Xu L L. An improved first-order primal-dual algorithm with a new correction step[J]. J Global Optim, 2013, 57(4):1419-1428.
[15] He B S. PPA-like contraction methods for convex optimization:A framework using variational inequality approach[J]. J Oper Res Soc China, 2016, 3(4):391-420.
[16] Yin W T, Osher S, Goldfarb D, Darbon J. Bregman iterative algorithms forl1-minimization with applications to compressed sensing[J]. SIAM J Imaging Sci, 2008, 1:143-168.
[17] Cai J F, Osher S, Shen Z W. Linearized bregman iterations for compressed sensing[J]. Math Comput, 2009, 78(267):1515-1536.
[18] Wright S J, Nowak R D, Figueiredo M A T. Sparse reconstruction by separable approximation[J]. IEEE Trans Signal Proc, 2009, 57(7):2479-2493.
[19] Shen Y, Wang C J. A self-adaptive projection and contraction method for optimizing the sum of a convex and a quadratic function[J]. Pacific J Optim, 2013, 9(1):137-154.
[1] 徐海文, 孙黎明. 一类凸优化的加速混合下降算法[J]. 计算数学, 2017, 39(2): 200-212.
[2] 徐海文. 一类凸优化的混合下降算法[J]. 计算数学, 2012, 34(1): 93-102.
[3] 郑雄波, 张晓威. 多小波变换在声纳图像降噪中的应用研究[J]. 计算数学, 2011, 32(2): 89-96.

Copyright 2008 计算数学 版权所有
中国科学院数学与系统科学研究院 《计算数学》编辑部
北京2719信箱 (100190) Email: gxy@lsec.cc.ac.cn
本系统由北京玛格泰克科技发展有限公司设计开发
技术支持: 010-62662699 E-mail:support@magtech.com.cn
京ICP备05002806号-10