一种基于偏微分方程变分去噪模型  

An Denoising Model of Variation Based on PDE

作　　者：张哲[1] 张化朋[1] 

机构地区：[1]南京邮电大学理学院,江苏南京210046

出　　处：《计算机技术与发展》2014年第11期103-106,共4页Computer Technology and Development

基　　金：国家自然科学基金资助项目(11301281)

摘　　要：近年来,国内外学者对于泊松噪声的研究越来越多,在TV模型的基础上提出了不少二阶去噪模型,它们在有效去除噪声的同时,很好地保护了图像边缘细节,但是共同的缺点是产生了"块效应"。针对这一不足,文中提出了一种四阶去噪模型,运用变分原理得到了其相应的欧拉拉格朗日方程,并用梯度下降法求解拉格朗日方程。文中运用差分法对该模型进行了数值求解与仿真,实验结果表明,提出的方法不仅去噪效果良好,而且有效改善了二阶去噪模型中出现的"块效应",同时有效保护了边缘细节。In recent years,there are more and more studies on Poisson noise by domestic and foreign scholars,they have proposed several second-order derivative denoising models based on TV model,which are able to remove the noise effectively,and at the same time,pro-tect the image edge detail well,but have a common drawback called＆quot;block effect＆quot;. In response to this deficiency,propose a fourth-order denoising model in this paper,and use the variational principle to get its corresponding Euler Lagrange equation and apply the gradient de-scent method to solve the equation. In this paper,use the differentiated method for numerical solution of the model and simulation,the re-sults show that the proposed method not only removes the noise effectively,but also improve the block effect while protecting the edge detail.

关 键 词：变分方法 偏微分方程 图像去噪 泊松噪声 四阶模型 块效应 

分 类 号：TP31[自动化与计算机技术—计算机软件与理论]