中文摘要：

从局部扩散角度分析了经典变分PDE复原模型的不足，给出一种基于全变差模型和调和模型的混合图像复原模型，并导出了相应的数字混合滤波器．该滤波器可以根据图像的局部梯度特征自适应选取滤波器系数，能在去噪的同时保留边缘，并削弱平滑区域的阶梯效应，具有较好的综合性能．针对该混合滤波器，还设计出相应的图像修补和放大算法．大量仿真实验表明，该滤波器可以很好地应用于图像的去噪、修补和放大．

英文摘要：

The drawbacks of the classical variational PDE image restoration models are analyzed from the view of local diffusion in this paper. Then a hybrid image restoration model based on the total variational model and the harmonic model is proposed and its corresponding digital filter is deduced. A hybrid filter is proposed can select coefficients adaptively according to the local gradient of the image. The proposed hybrid filter can not only denoise while preserving edges, but also reduce the staircase effect in smooth regions. Finally, based on the hybrid filter, a generalized algorithm for image denoising, inpainting and zooming is developed. The proposed algorithm has been evaluated qualitatively and quantitatively on several various types of images produced from such as natural and remote sensing.