Asymmetry total variation and framelet regularized nonconvex low-rank tensor completion

The low-rank tensor representation has shown enormous potential and advantages in diverse applica-tions, such as image inpainting, image restoration. However, (1) due to the inherent limitations of the low-rank tensor model, the tensor nuclear norm is utilized yet as a biased estimate of the tensor rank, which limits the image recovery performance. (2) most current low-rank approximation-based meth-ods focus on the preservation of global information, while ignoring the local details preservation such as the spatial piece-wise smoothness and sharp edges. To overcome the above obstacles, we propose a novel asymmetry three-dimensional total variation and framelet regularized nonconvex low-rank tensor completion (ATV-FNTC) model, which integrates the nonconvex penalty function and asymmetric three-dimensional total variation into one unified model. Specifically, ATV-FNTC introduces one nonconvex penalty function as a tighter regularizer to approximate the tensor rank. Different from existing meth-ods, the asymmetric three-dimensional total variation (ATV) regularization is developed to achieve more accurate recovery of detailed information and flexibly control the smoothing strength of different dimen-sions of tensor data. Furthermore, we design an iterative algorithm to solve the nonconvex ATV-FNTC model by the alternating direction methods of multipliers. Experimental results reveal the superiority of the proposed method compared with several state-of-the-art methods when handling different comple-tion tasks.(c) 2022 Published by Elsevier B.V.