基于Gabor变换和组稀疏表示的敦煌壁画修复算法

Algorithm for Dunhuang Mural Inpainting Based on Gabor Transform and Group Sparse Representation

在敦煌壁画修复过程中,初始字典的随机选取易陷入局部最优,仅以颜色欧氏距离作为图像块分组标准会导致图像修复后易出现结构模糊和线条不连续等问题。针对以上问题,提出了一种基于Gabor变换和组稀疏表示的敦煌壁画修复算法。首先,采用互信息作为图像块分组准则,并建立相似结构组,这使得组稀疏表示更加合理;然后,通过Gabor小波变换对相似结构组进行特征信息提取,并结合PCA降维的方式得到初始化结构组的特征字典,避免了字典初始化随机选取的不足;最后,采用奇异值SVD分解和分裂Bregman迭代优化方法对结构组字典和稀疏系数进行学习并完成壁画图像的修复。实验结果表明,相比于其他对比算法,所提方法取得了较好的主客观修复效果。

In the process of Dunhuang mural restoration,dictionary initialized random selection falls into local optimum easily and only the color Euclidean distance is used as the standard for image block grouping,which leads to the problems such as structure blur and line discontinuity after image restoration.An algorithm for Dunhuang mural inpainting based on Gabor transform and group sparse representation is proposed in this paper.First,the similar structure group is established using mutual information as the criterion of image block grouping,which makes group sparse representation more reasonable.Second,the Gabor wavelet transform is used to extract the feature information of similar structure groups,and the feature dictionary of the structure group is initialized by means of PCA dimension reduction,which can avoid the disadvantage of dictionary initialized random selection.Finally,the SVD decomposition and the split Bregman iteration method are used to learn the structure group dictionary and the sparse coefficients to complete the mural image restoration.The experimental results show that,compared with the other algorithms,the algorithm proposed in this paper has achieved good subjective and objective restoration effects.