中文摘要：

为保护图像的几何结构，该文提出加权的小波变分修复模型。该模型充分利用权函数在平滑区域增强去噪，在边缘处保护边缘等特性来增强图像的修复效果。为有效地计算该模型，首先利用交替方向法将该模型化为两个子模型，然后再对两个子模型分别给出相应的算法。数值实验表明，新模型不仅在视觉上，而且在信噪比上均取得了较好的结果。

英文摘要：

In order to preserve the geometric characteristics of image, a weighted wavelet variational inpainting model is proposed. The new model makes use of the advantages of weighted function that can improve the capacity for denoising in the smooth region and protect the edges in the edge region, so it can enhance the inpainting effect. To solve the proposed model effectively, it is firstly turned into two submodels using alternating direction method, then the corresponding theoretical derivation and algorithms are given. The numerical experiments show that the new model can not only get the better visual effect, but also obtain the higher Signal to Noise Ratio （SNR） than the recent total variation wavelet inpainting method.