原始-对偶模型的牛顿迭代原理与图像恢复

doi:10.3969/j.issn.0372-2112.2015.10.016

电子学报 ›› 2015, Vol. 43 ›› Issue (10): 1984-1993.DOI: 10.3969/j.issn.0372-2112.2015.10.016

原始-对偶模型的牛顿迭代原理与图像恢复

李旭超¹, 宋博²

1. 赤峰学院计算机与信息工程学院, 内蒙古赤峰 024000;
2. 江苏师范大学电气工程及自动化学院, 江苏徐州 221116

收稿日期:2014-10-07 修回日期:2015-01-12 出版日期:2015-10-25
- 作者简介:
- 李旭超 男,1974年12月出生于内蒙古赤峰市.现为赤峰学院计算机与信息工程学院教师,从事调和分析方面的研究工作.E-mail:bsx7096@sohu.com;宋博男,1979年12月出生于江苏省徐州市.现为江苏师范大学电气工程及自动化学院教师,从事随机控制理论、时滞系统方面的研究工作.E-mail:songboxuzhou@sohu.com
- 基金资助:
- 国家自然科学基金 (No.61104221); 江苏省高校自然科学基金 (No.10KJB120004); 江苏师范大学博士人才基金 (No.10XLR27)

Newton Iterative Principle of Primal-Dual Model and Image Restoration

LI Xu-chao¹, SONG Bo²

1. College of Computer and Information Engineering, Chifeng University.Chifeng, Mongola 024000, China;
2. College of Electrical Engineering and Automation, Jiangsu Normal University.Xuzhou, Jiangsu 221116, China

Received:2014-10-07 Revised:2015-01-12 Online:2015-10-25 Published:2015-10-25
- Supported by:
- National Natural Science Foundation of China (No.61104221); Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No.10KJB120004); Doctoral Talent Fund of Jiangsu Normal University (No.10XLR27)

摘要/Abstract

摘要：

针对非可微有界变差函数容易在图像恢复过程产生阶梯效应,提出一种二阶可微的原始-对偶模型及牛顿迭代算法.分析伪Huber函数的特性,运用Fenchel变换,将原始模型转化为原始-对偶模型,然后提出原始与对偶变量不同步长更新策略的牛顿迭代算法,并给出广义交叉验证准则确定权重.利用点扩散函数和高斯噪声对合成与真实图像进行模糊,将本文方法与快速傅里叶变换算法、快速收缩阈值算法、交替投影算法和拟牛顿算法进行实验对比,仿真表明,本文算法能保护图像的边缘,抑制阶梯效应,取得较小的相对误差、偏差,较高的峰值信噪比、相似度性测度和良好的视觉效果.

关键词: 原始-对偶模型, 图像恢复, 能量泛函, 算法收敛

Abstract:

For non-differential characteristics and easily producing stair effect of total variation in image restoration, the paper presents a second order differential primal-dual model and Newton iterative algorithm.The characteristics of pseudo Huber function are analyzed, primal model is converted into primal-dual model resort to Fenchel transform, Newton iterative algorithm based on the different step length update schemes of primal and dual variables are proposed, and the generalized cross validation principle is given to determine the weight.Synthesized and real images are blurred by point spread function and Gaussian noise, the comparison experiments among the proposed scheme with fast Fourier transform algorithm, fast shrinkage-thresholding algorithm, alternating projection algorithm and quasi-Newton algorithm are carried out.Simulation results show the proposed algorithm can protect image edges, alleviate stair effect, and achieve lower relative error and deviation, higher peak signal to noise ratio and structural similarity index measure, and better visual effect.

Key words: primal-dual model, image restoration, energy functional, algorithm convergence

中图分类号:

TP302.7

李旭超, 宋博. 原始-对偶模型的牛顿迭代原理与图像恢复[J]. 电子学报, 2015, 43(10): 1984-1993.

LI Xu-chao, SONG Bo . Newton Iterative Principle of Primal-Dual Model and Image Restoration[J]. Acta Electronica Sinica, 2015, 43(10): 1984-1993.

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原始-对偶模型的牛顿迭代原理与图像恢复

Newton Iterative Principle of Primal-Dual Model and Image Restoration

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