Low-rank tensor completion via nonlocal self-similarity regularization and orthogonal transformed tensor Schatten-p norm

Abstract

Low-rank tensor completion (LRTC) has become more and more popular in the field of tensor completion. Because solving the tensor rank minimization is NP-hard, extensive surrogate norms of tensor rank have been proposed successively. Among these norms, the innovative nonconvex orthogonal transformed tensor Schatten-p norm (OTT\(S_{p}\)) can better capture the low-rank property of tensor than most competitive norms. However, the OTT\(S_{p}\) method solely depends on the global low-rank prior and ignores the importance of the nonlocal similar structures, which play a significant role in the tensor data processing. In this paper, to address the defect of the OTT\(S_{p}\) method, we propose a novel LRTC model based on nonlocal self-similarity (NSS) regularization, which combines NSS regularization with the OTT\(S_{p}\). As a nonlocal prior, NSS can preserve the nonlocal similar details, so the introduction of NSS regularization contributes to promoting the final inpainting performance. Therefore, our proposed model is capable of further conserving nonlocal self-similarities based on the global low-rankness. Moreover, the alternating direction method of multipliers is adopted to solve our proposed model. Experimental results on color images, grey-scale videos, and multispectral images demonstrate the superiority of our proposed method compared with other existing state-of-the-art methods.