基于8-邻域和曲率的多阶偏微分方程混合去噪

Hybrid Denoising of Multi-order Partial Differential Equations Based on 8-Neighborhood and Curvature

为解决二阶偏微分方程图像去噪时产生的阶梯效应,考虑到四阶偏微分方程在图像光滑区域消除阶梯效应的能力,提出基于8-邻域和隐式曲率的多阶偏微分方程混合去噪方法,利用8-邻域和隐式曲率构造的权重函数去控制两类方程在图像去噪时的比例,实现二阶偏微分方程和四阶偏微分方程的自适应调整去噪。实验结果表明,新方法能有效避免边缘模糊和“阶梯效应”又能消除四阶偏微分方程的“斑点效应”,图像的MAE、PSNR、SSIM值显著提升,去噪效果较好,且能够较好保持图像细节特征和边缘信息。

In order to solve the step effect of second-order partial differential equation image denoising,considering the ability of fourth-order partial differential equation to eliminate the step effect in smooth image area,a hybrid denoising method of multi-order partial differential equation based on 8-neighborhood and implicit curvature is proposed. The ratio of two kinds of equations in image denoising is controlled by using the weight function constructed by 8-neighborhood and implicit curvature,and the adaptive denoising of second-order partial differential equation and fourth-order partial differential equation is realized. The experimental results show that the new method can effectively avoid edge blurring and "staircase effect" and eliminate the "speckle effect" of the fourth-order partial differential equation. The MAE,PSNR and SSIM values of the image are significantly improved,the denoising effect is good,and the details and edge information of the image can be well maintained.