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

The low-rank tensor representation has shown enormous potential and advantages in diverse applications, 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 methods 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 methods, 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 dimensions 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 completion tasks.