Variational noise removal method based on second-order and fourth-order PDEs

doi:10.3778/j.issn.1002-8331.2010.25.045

Computer Engineering and Applications ›› 2010, Vol. 46 ›› Issue (25): 153-156.DOI: 10.3778/j.issn.1002-8331.2010.25.045

• 图形、图像、模式识别 • Previous Articles Next Articles

Variational noise removal method based on second-order and fourth-order PDEs

ZHANG Jiu-xing^1，2，HEI Bao-qin¹，LI Sheng-yang1

1.Payload Operation and Application Center，Academy of Opto-Electronics，Chinese Academy of Sciences，Beijing 100190，China
2.Graduate University of Chinese Academy of Sciences，Beijing 100049，China

Received:2010-01-22 Revised:2010-03-26 Online:2010-09-01 Published:2010-09-01
Contact: ZHANG Jiu-xing

一种基于二阶和四阶PDEs的变分去噪方法

张九星^1，2，黑保琴¹，李盛阳¹

1.中国科学院光电研究院有效载荷应用中心，北京 100190
2.中国科学院研究生院，北京 100049

通讯作者: 张九星

Abstract

Abstract: The image noise removal methods based on second-order PDEs（Partial Differential Equations） can remove noise while protecting edges well，but produce staircase effects in the smooth regions of image，and the methods based on fourth-order PDEs can avoid staircase effects.A variational noise removal method based on second-order and fourth-order PDEs has been presented，and its Eular equation and gradient descent flow have been shown，meanwhile its numerical schemes are analyzed.According to noise removal experiments，it is proven that this method can remove noise effectively and protect edges to a certain extent，at the same time，staircase effects are restrained efficiently，and the quality of noisy image is improved.

Key words: second-order, fourth-order, variation, image noise removal, partial differential equations

摘要： 二阶偏微分方程图像去噪方法在去除噪声同时保护边缘效果较好，但在平滑区会产生阶梯效应，而四阶方法可以消除阶梯效应，基于此提出了一种将二阶与四阶偏微分方程相结合的变分去噪方法，给出了其欧拉方程和梯度下降流，并分析了数值离散化方法。通过去噪实验表明，该方法能有效去除噪声干扰，在一定程度上保护边缘，并且可以有效减弱阶梯效应，改善图像质量。

关键词: 二阶, 四阶, 变分, 图像去噪, 偏微分方程

CLC Number:

TP391.41

ZHANG Jiu-xing^1，2，HEI Bao-qin¹，LI Sheng-yang1. Variational noise removal method based on second-order and fourth-order PDEs[J]. Computer Engineering and Applications, 2010, 46(25): 153-156.

张九星^1，2，黑保琴¹，李盛阳¹. 一种基于二阶和四阶PDEs的变分去噪方法[J]. 计算机工程与应用, 2010, 46(25): 153-156.

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Variational noise removal method based on second-order and fourth-order PDEs

一种基于二阶和四阶PDEs的变分去噪方法

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