一种基于偏微分方程变分去噪模型

An Denoising Model of Variation Based on PDE

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.