Abstract: In order to denoise the nosiy image and overcome the staircase effect which is often produced by total variation denoising method, a new image denoising method based on the improved second order Total Generalized Variation（TGV）is proposed. Firstly, the theory of second order TGV is presented. Then, an anisotropic diffusion tensor is introduced in the regularization term of second order TGV. The new proposed model is utilized the tensor function to guide the diffusion. At last, an extended primal-dual algorithm is proposed to solve the new model numerically. The new model combines the advantages such as the second order TGV regularization which can automatically balance the first order and second order derivative, the diffusion tensor which can strengthen the edges structures. Experimental results indicate that the proposed method can effectively remove the noise and avoid the staircase effect while preserving the edges of image.

Key words: image denoising, total generalized variation, anisotropic diffusion tensor, primal-dual algorithm

摘要： 为了有效地去除含噪图像中的噪声，克服总变分（TV）去噪易于导致阶梯效应的缺陷，提出了一种改进的二阶总广义变分（TGV）的图像去噪方法。介绍了二阶TGV的理论基础，在二阶TGV中引入了各向异性扩散张量，利用张量函数引导扩散，获得了新的去噪模型，最后提出了一种扩展了的原始-对偶算法对新模型进行数值求解。新模型充分结合了二阶TGV作为正则项自动平衡了一阶和二阶导数项，以及张量函数的各向异性扩散，有效突出边缘结构的特性。实验结果表明，该方法在有效地去除含噪图像中噪声的同时，避免了阶梯效应，增强了对原始图像中边缘结构的保持。

关键词: 图像去噪, 总广义变分, 各向异性扩散张量, 原始-对偶算法