| 一种基于二阶和四阶PDEs的变分去噪方法 |
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| 引用本文： | 张九星,黑保琴,李盛阳.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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| 作者姓名： | 张九星 黑保琴 李盛阳 |
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| 作者单位： | 1. 中国科学院,光电研究院,有效载荷应用中心,北京,100190;中国科学院,研究生院,北京,100049
2. 中国科学院,光电研究院,有效载荷应用中心,北京,100190 |
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| 基金项目： | 国家自然科学基金青年科学基金项目资助 |
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| 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。
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| 关 键 词： | 二阶 四阶 变分 图像去噪 偏微分方程 |
| 收稿时间： | 2010-1-22 |
| 修稿时间： | 2010-3-26
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Variational noise removal method based on second-order and fourth-order PDEs |
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| ZHANG Jiu-xing,HEI Bao-qin,LI Sheng-yang.Variational noise removal method based on second-order and fourth-order PDEs[J].Computer Engineering and Applications,2010,46(25):153-156. |
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| Authors: | ZHANG Jiu-xing HEI Bao-qin LI Sheng-yang |
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| Affiliation: | 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) |
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| 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. |
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| Keywords: | second-order fourth-order variation image noise removal partial differential equations |
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