基于偏微分方程的含噪图像复原新模型

A New Image Restoration Model Based on Partial Differential Equation

针对现有的用于图像复原的全变分和四阶偏微分方程模型存在的不足,提出一种图像复原新模型。新模型的思想是将全变分和四阶偏微分方程模型相结合,同时通过修改方程中的一个扩散项的系数,来达到增强去噪效果的目的。新模型弥补了经典图像复原方法的不足,既保护了图像边缘,又抑制了"阶梯效应",且具有较高的信噪比。理论分析和MATLAB仿真结果表明,经过新模型复原的图像质量较高,具有良好的视觉效果,充分体现了新模型在图像复原上的有效性。

Aiming at the shortcomings of the existing total variation and fourth order partial differential equation（PDE）image restoration model,a new image restoration model is put forward.The ideal of the new model is to combine the two models,at the same time,by modifying a diffusion coefficient of the equation,to achieve the enhancement purpose to the effect of image denoising.The new model not only makes the image edge details be protected and the＂ladder effect＂be restrained,but also has high signal-to-noise ratio.Theoretical analysis and MATLAB simulation results show that the recovery image quality is higher after the new model dispose,and also have a good visual effect,fully embodying the effectiveness of the new model on image restoration.