中文摘要：

自适应正则化方法在不同的局部区域能够选取不同的正则化参数和正则化约束,因而能够灵活地对边缘和噪声进行区别处理。将自适应正则化建立在图上,提出了一种定义在加权图上的,具有自适应参数的正则化模型。用nonlocal means算法构造图的权重函数,用建立在图上的自适应正则化方程实现图像的去噪处理,仿真实验结果表明：该方法能有效地去除图像中的噪声,在去噪性能上优于部分基于图论的偏微分方程方法。

英文摘要：

Adaptive regularization can select different parameters based on the features of local areas in an image, which can differentiate the edges and noise in an image flexibly. An adaptive graph regularization is proposed based on graph spectral theory and adaptive regularization, which uses the Non local means to generate the weighting function of graph. The adaptive graph regularization equation is used to filter the noisy image. Simulation results show that the proposed method can effectively remove the noise and is superior to other graph theory based partial differential equation methods.