Newton Iterative Principle of Primal-Dual Model and Image Restoration

LI Xu-chao; SONG Bo

doi:10.3969/j.issn.0372-2112.2015.10.016

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Newton Iterative Principle of Primal-Dual Model and Image Restoration

更新时间：2025-07-16

- Newton Iterative Principle of Primal-Dual Model and Image Restoration
- Acta Electronica Sinica Vol. 43, Issue 10, Pages: 1984-1993(2015)
- 作者机构：
  
  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
  3. 赤峰学院计算机与信息工程学院,内蒙古,赤峰,024000
  4. 江苏师范大学电气工程及自动化学院,江苏,徐州,221116
- 作者简介：
- 基金信息：
  
  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)
- DOI：10.3969/j.issn.0372-2112.2015.10.016
  CLC： TP302.7
- Published：2015
- 稿件说明：
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LI Xu-chao, SONG Bo. Newton Iterative Principle of Primal-Dual Model and Image Restoration[J]. Acta Electronica Sinica, 2015, 43(10): 1984-1993.
DOI：

LI Xu-chao, SONG Bo. Newton Iterative Principle of Primal-Dual Model and Image Restoration[J]. Acta Electronica Sinica, 2015, 43(10): 1984-1993. DOI： 10.3969/j.issn.0372-2112.2015.10.016.

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.

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.

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