多尺度轮廓波分解的群稀疏壁画修复算法

Mural inpainting algorithm for group sparse based on multi-scale contourlet transform decomposition

壁画图像修复是利用原始壁画图像的先验信息从缺失像素的破损壁画出发恢复原始图像的过程。针对稀疏表示在壁画图像修复时,未考虑壁画结构信息与纹理信息的差异性,导致修复结果易出现纹理模糊和结构线条断裂等问题,提出了一种基于多尺度轮廓波分解的群稀疏壁画修复算法。首先,采用非下采样轮廓波变换对待修复壁画图像进行多尺度分解,将其分解为低频纹理分量和高频结构分量,克服了现有稀疏表示壁画修复时,未考虑壁画结构和纹理信息差异性的不足。其次,采用提出的改进群稀疏算法,对纹理低频分量构造样本块相似群集合,并通过奇异值分解和分裂伯格曼算法迭代优化得到自适应群字典和稀疏系数,从而完成低频分量的修复。然后,使用三次立方卷积插值算法实现对壁画结构高频分量的插值修复。最后,通过非下采样轮廓波逆变换对修复后各尺度分量进行融合重构。通过对真实敦煌壁画的修复实验,结果表明,所提方法相较对比算法取得了更好的主客观修复效果及评价。

Mural image restoration is a process of recovering the original image from the damaged mural with missing pixels by using the prior information on the original mural image.In view of the problem that sparse representation does not consider the difference between mural structure information and texture information in mural image restoration, resulting in texture blur and structural line fracture, a group sparse mural restoration algorithm based on multi-scale contour wave decomposition is proposed.First, the nonsubsampled contourlet transform is used to decompose the mural image to be repaired into the low-frequency texture component and high-frequency structure component, which overcomes the deficiency that the difference of mural structure and texture information is not considered in the existing sparse representation of mural repair.Then, the proposed improved group sparse algorithm is used to construct the similar group set of sample blocks for the low-frequency components of texture, and the adaptive group dictionary and sparse coefficients are obtained through the iterative optimization of singular value decomposition and the split Bregman iteration algorithm, so as to complete the repair of low-frequency components.Second, the cubic convolution interpolation algorithm is used to realize the interpolation repair of the high-frequency components of the mural structure.Finally, the restored scale components are fused and reconstructed by the inverse transform of the non down sampled contour wave.Through the restoration experiment of real Dunhuang murals, the results show that the proposed method achieves a better subjective and objective restoration effect and evaluation than the comparison algorithm.