改进的迭代算法在图像恢复正则化模型中的应用

doi:10.3969/j.issn.0372-2112.2015.06.017

电子学报 ›› 2015, Vol. 43 ›› Issue (6): 1152-1159.DOI: 10.3969/j.issn.0372-2112.2015.06.017

改进的迭代算法在图像恢复正则化模型中的应用

李旭超¹, 宋博², 甘良志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:2014-05-06 修回日期:2014-08-25 出版日期:2015-06-25 发布日期:2015-06-25
作者简介:李旭超 男,1974年出生,内蒙古赤峰市人,现为赤峰学院计算机与信息工程学院教师.研究方向为调和分析在信息处理中的应用. E-mail:bsx7096@sohu.com; 宋博 男,1979年出生,江苏徐州市人,现为江苏师范大学电气工程及自动化学院教师.研究方向为随机控制理论、时滞系统在信息处理中的应用.
基金资助:
国家自然科学基金(No.61104211);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)

The Application of Improved Iterative Algorithm to Regularization Model of Image Restoration

LI Xu-chao¹, SONG Bo², GAN Liang-zhi²

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

Received:2014-05-06 Revised:2014-08-25 Online:2015-06-25 Published:2015-06-25

摘要/Abstract

摘要：

根据图像成像过程容易受泊松噪声的影响,提出用Kullback-Leibler距离描述保真项,用平方根复合函数描述正则项,建立具有自适应权系数的能量泛函正则化模型.由于模型的梯度退化和海森矩阵的规模较大,使得无法应用牛顿迭代算法.本文利用退化梯度幅值作为约束集,建立可对角化和容易求逆的海森矩阵,提出改进的牛顿投影迭代算法.仿真表明,该方法取得较小的相对误差、偏差,较高的信噪比和良好的视觉效果.

关键词: 正则化, 图像恢复, 海森矩阵, 活跃集

Abstract:

According to the imaging process is easily affected by Poisson noise, the image restoration regularization model that fidelity term is described by Kullback-Leibler Euclidean and the regularization term is established by the square root compound function, with adaptive weight coefficients, is proposed.For the gradient degeneration and the large scale Hessian matrix, it is unable to apply the Newton iterative algorithm to the model.In this paper, constraint set is introduced by the magnitude value of degeneration gradient, the diagonal and easily computed Hessian matrix is established, and the improved Newton iterative projection algorithm is proposed.Simulation results show the proposed can effectively restore image, such as the lower relative error and deviation, the higher peak signal to noise ratio, and better visual effect.

Key words: regularization, image restoration, Hessian matrix, active set

中图分类号:

TP302.7

李旭超, 宋博, 甘良志. 改进的迭代算法在图像恢复正则化模型中的应用[J]. 电子学报, 2015, 43(6): 1152-1159.

LI Xu-chao, SONG Bo, GAN Liang-zhi. The Application of Improved Iterative Algorithm to Regularization Model of Image Restoration[J]. Acta Electronica Sinica, 2015, 43(6): 1152-1159.

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改进的迭代算法在图像恢复正则化模型中的应用

The Application of Improved Iterative Algorithm to Regularization Model of Image Restoration

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