去除乘性噪声的迭代重加权二阶正则模型

doi:10.3969/j.issn.1001-2400.2014.02.022

J4 ›› 2014, Vol. 41 ›› Issue (2): 130-136.doi: 10.3969/j.issn.1001-2400.2014.02.022

去除乘性噪声的迭代重加权二阶正则模型

王旭东^1,2;冯象初¹;张选德^1,3

(1. 西安电子科技大学数学与统计学院，陕西西安 710071;
2. 广西科技大学理学院，广西柳州 545006;
3. 宁夏大学数学计算机学院，宁夏银川 750021)

收稿日期:2012-12-10 出版日期:2014-04-20 发布日期:2014-05-30
通讯作者: 王旭东
作者简介:王旭东(1973- )，男，西安电子科技大学博士研究生，E-mail: xudwang@mail.xidian.edu.cn．
基金资助:
国家自然科学基金资助项目(61271294，60872138，61105011，11101292，61001156，61362029)

Iteratively reweighted second-order regularization based multiplicative noise removal model

WANG Xudong^1,2;FENG Xiangchu¹;ZHANG Xuande^1,3

(1. School of Mathematics and Statistics, Xidian Univ., Xi'an 710071， China;
2. School of Science, Guangxi Univ. Science and Technology, Liuzhou 545006， China;
3. School of Mathematics and Computer Science, Ningxia Univ., Yinchuan 750021， China)

Received:2012-12-10 Online:2014-04-20 Published:2014-05-30
Contact: WANG Xudong

摘要/Abstract

摘要：

为了去除图像中乘性噪声的影响，在乘性噪声服从伽玛(Gamma)分布的假设下，提出了迭代重加权二阶导数(Hessian矩阵F范数)正则模型，从而推广了迭代重加权全变差正则模型．然后对迭代重加权Hessian矩阵F范数正则模型建立了原始-对偶算法．数值实验表明，文中模型和算法能够在有效去除噪声的同时，较好地保留图像的细节，抑制阶梯效应并避免边缘模糊．

关键词: 图像去噪, 乘性噪声, 扩散, Hessian矩阵, 原始-对偶算法

Abstract:

In order to remove the multiplicative noise in an image, an iteratively reweighted second order derivatives(Frobenius norm of Hessian matrix) regularization model is proposed under the assumption that the multiplicative noise follows a Gamma distribution, which is an extension of the iteratively reweighted total variation model. A primal-dual algorithm for iteratively reweighted Frobenius norm of the Hessian matrix regularization model is designed. Numerical experiments show that the proposed model and algorithm can remove noise effectively while preserving details, restraining the staircase effect and avoiding edge blurring.

Key words: image denoising, multiplicative noise, diffusion, Hessian matrix, primal-dual algorithm

王旭东;冯象初;张选德. 去除乘性噪声的迭代重加权二阶正则模型[J]. J4, 2014, 41(2): 130-136.

WANG Xudong;FENG Xiangchu;ZHANG Xuande. Iteratively reweighted second-order regularization based multiplicative noise removal model[J]. J4, 2014, 41(2): 130-136.

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去除乘性噪声的迭代重加权二阶正则模型

Iteratively reweighted second-order regularization based multiplicative noise removal model

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