To overcome the “staircase effect” while preserving the structural information such as image edges and textures quickly and effectively, we propose a compensating total variation image denoising model combining L₁ and L₂ norm. A new compensating regular term is designed, which can perform anisotropic and isotropic diffusion in image denoising, thus making up for insufficient diffusion in the total variation model. The algorithm first uses local standard deviation to distinguish neighborhood types. Then, the anisotropic diffusion based on L₁ norm plays the role of edge protection in the strong edge region. The anisotropic and the isotropic diffusion simultaneously exist in the smooth region, so that the weak textures can be protected while overcoming the “staircase effect” effectively. The simulation experiments show that this method can effectively improve the peak signal-to-noise ratio and obtain the higher structural similarity index and the shorter running time.

为了克服“阶梯效应”，同时快速有效地保留图像边缘和纹理等结构信息，我们提出了一种结合L ₁和L ₂范数的补偿总变化图像去噪模型。设计了一种新的补偿正则项，可以在图像去噪中进行各向异性和各向同性扩散，从而弥补了总变化模型中的扩散不足。该算法首先使用局部标准差来区分邻域类型。然后，基于L ₁的各向异性扩散规范在强边缘区域中起到边缘保护的作用。各向异性和各向同性扩散同时存在于光滑区域中，因此可以有效地克服“楼梯效应”的同时保护弱纹理。仿真实验表明，该方法可以有效提高峰值信噪比，获得较高的结构相似指数和较短的运行时间。