Abstract: To improve the edge preserving ability of current high order models, this paper proposes a new high order variational energy function by introducing the gradient information after convolution as the weighting function of second derivative, and leads to a fourth-order partial differential equation diffusion model. In the procedure of constructing the weighting coefficients, this paper gives a scheme that makes weighting function have the ability to preserve a certain edge based on the analysis of classical second-order total variation diffusion model. This weighting function can determine local structure region of the image and adapt the diffusion rate, as well as avoid boundary oscillations with good retention properties of the detail. The experimental results show that the proposed model can relief staircase effect, avoid oscillations and preserve edges while removing noise.

Key words: image denoising, high order variational model, regularization term, edge preserving, staircase effect

摘要： 针对现有高阶变分模型不能很好保持边界的问题，引入卷积后的一阶梯度信息作为二阶导数的加权函数，建立了一个新的高阶变分能量泛函，并得到了四阶偏微分方程扩散模型。在加权系数的构造中，在分析经典二阶全变分扩散模型结构的基础上，给出了具有一定边缘保持能力的加权函数设计方案。此加权函数可判断图像局部区域结构，自适应调整扩散速度，有利于在扩散中保留细节。数值实验表明，该模型可以有效去除噪声，消除阶梯效应，避免边界振荡，具有较好的边界保持性质。

关键词: 图像去噪, 高阶变分模型, 正则项, 边界保持, 阶梯效应