Image inpainting algorithm based on tensor decomposition and weighted nuclear norm

For a damaged image, recovering an image with missing entire rows or columns is a challenging problem arising in many real applications, such as digital image inpainting. For this kind of information missing situation, the diffusion-based inpainting methods are tend to produce blur, the exemplar-based methods are prone to error filling and the neural network-based methods are highly dependent on data. Many existing approaches formulate this problem as a general low-rank matrix approximate one which cannot handle this special structural missing very well. In this paper, we propose a novel image inpainting algorithm named nonlocal low-rank tensor completion (NLLRTC) based on the nonlocal self-similarity prior and the low-rank prior. By using the nonlocal self-similarity of image patches, we directly stack these patches into a three-dimensional similar tensor instead of pulling them into column vectors, then the similar tensor can be completed by tensor ring (TR) decomposition. By leveraging the alternating direction method under the augmented Lagrangian multiplier framework, the optimization results can be obtained. Moreover, a weighted nuclear norm is added to the tensor completion model to achieve better inpainting performance, which we call weighted nonlocal low-rank tensor completion (WNLLRTC) algorithm. Our empirical studies show encouraging results on both quantitative assessment and visual interpretation of our proposed methods in comparison to some state-of-the-art algorithms.