关键词: 稀疏先验, 矩阵补全, 截断Schatten-p范数, 图像修复, 交替方向乘子法

Abstract: To handle the problem that the image matrix completion algorithm based on low rank prior cannot effectively deal with the structural missing image inpainting, a matrix completion model using double prior on the observation matrix was established. The sparse prior was integrated with low rank prior, so as to make better use of the prior characteristics of the observation matrix. The model used low rank prior and sparse prior to regularize the matrix by using the correlation between rows and columns and within the row and column, respectively. Furthermore, in order to more accurately approximate the rank function, the truncated Schatten-p norm was used to replace the nuclear norm as the low rank prior. Thus, a matrix completion model integrating low rank and sparse prior was proposed, and the alternating direction method of multiplier was used to solve the proposed completion model effectively. The experimental results show that the details of the inpainting image are clear. Compared with the truncated nuclear norm model algorithm, the corresponding improvement ranges of peak signal-to-noise ratio and structure similarity are 2%-44% and 0.7%-8%, respectively.

Key words: sparse prior, matrix completion, truncated Schatten-p norm, image inpainting, alternating direction method of multipliers