Abstract: The paper illustrates a function of describing image restoration based on Partial Differential Equation(PDE),and deduces new PDE image restoration model.It can eliminate noise perfectly and keep the characteristic of the image nicely.Compared with other classical restorational methods,the new model has advantage in theory.Moreover,it effectively sovles the contradiction between keeping edge and smoothing excessively.The simulation shows that the new model can perfectly restore image and keep the edge characteristic of the image nicely.

Key words: image restoration, Partial Differential Equation(PDE), total variation

摘要： 首先基于偏微分方程（PDE）提出一个描述图像复原的泛函，并推导出新的PDE图像复原模型，该模型不仅复原效果良好，而且能较好地保持图像的特征。与其他经典的复原方法相比较，新模型具有理论上的优势；其次，有效地解决了保持图像边缘特征和图像的过度平滑这对矛盾。实验表明，给出的新模型既能较好地复原图像，又能很好地保持图像的边缘特征。

关键词: 图像复原, 偏微分方程, 全变分