改进多重字典联合自适应学习的稀疏壁画修复

Improved Sparse Mural Restoration Algorithm Using Joint Adaptive Learning of Multiple Dictionaries

针对壁画稀疏表示修复算法字典单一、细节修复欠佳的问题,提出了一种改进多重字典联合自适应学习的稀疏壁画修复算法.首先,采用非下采样剪切波NSST将破损壁画进行分解,获取壁画的低频纹理子带图像和高频结构子带图像,解决了稀疏表示算法对壁画图像结构和纹理信息考虑不足的问题.然后,提出了多重字典自适应学习的稀疏方法,将低频纹理图像根据像素之间特征的相似性进行聚类,构建多重稀疏子类字典,并利用奇异值分解和分裂Bregman迭代优化完成低频分量修复.接着,引入脉冲耦合神经网络机制,修复壁画图像的高频结构子带.最后,通过NSST逆变换融合完成修复.采用真实壁画进行修复的实验表明,该算法能够有效保护壁画图像结构和纹理层等重要信息,所提算法相较对比算法取得了更好的视觉效果和客观评价.

In repairing murals based on sparse representation,the dictionary construction is single,and the restoration of details is inadequate.Therefore,an improved sparse mural restoration algorithm using joint adaptive learning of multiple dictionaries is proposed.First,a non-subsampled shearlet transform(NSST)is used to perform multi-scale decomposition on the mural image to obtain low-frequency structural components and high-frequency texture components,overcoming the problem of neglecting the differences in texture and structure information in mural restoration using sparse representation.Then,a sparse method of multiple dictionary adaptive learning is proposed.The low-frequency texture image is clustered based on the similarity of features between pixels to construct multiple sparse sub-dictionaries,and the low-frequency component restoration is completed through singular value decomposition and split Bregman iteration optimization.Then,the pulse-coupled neural network mechanism is introduced to restore the high-frequency structural sub-band image of the mural image.Finally,the NSST inverse transform is used to merge and complete the restoration.Experimental results on actual murals show that the proposed algorithm effectively preserves significant information,such as the structure and texture layers of the mural image,and achieves better visual effects and objective evaluations than the compared algorithms.