Abstract: Due to transmission interference or improper storage, there exist some missing pixels in the images obtained in the real scene, which causes obstacles to the subsequent processing and analysis of the images. The key solution for missing pixels is to recover the image with low rank prior. However, since the rank function is discrete, the model that minimizes the rank is an NP-hard problem. In order to address this issue, a commonly used method is to employ an image-inpainting algorithm based on the nuclear norm. Unlike the methods based on the nuclear norm minimization, this paper proposed an image-inpainting algorithm using non-convex low-rank constraints, which replaced the traditional nuclear norm with a log function and overcame the inability of the nuclear norm to approach the rank minimization. In addition, to optimize the non-convex model, the augmented Lagrangian multiplier method was adopted to derive an alternating minimization algorithm. Experimental results demonstrate that the proposed method can deal with different missing pixel rates, and can far outperform other low-rank inpainting methods in inpainting. 

Key words: image inpainting, nuclear norm, alternating direction method of multiplier, non-convex and low-rank constraints, augmented Lagrangian method