Tensor p-shrinkage nuclear norm for low-rank tensor completion

摘要

In recent times, low-rank tensor completion (LRTC), which involves completing missing entries in partially observed tensors, is attracting significant attention from researchers. Several previously proposed LRTC methods have been successfully applied to practical applications. However, while the tensor nuclear norm has been successfully applied to solve the LRTC problem, penalizing all singular values equally restricts its recovery accuracy. In this study, we propose an efficient tensor p-shrinkage nuclear norm (p-TNN) based on tensor singular value decomposition (t-SVD). Under the condition -infinity < p < 1, we theoretically prove that p-TNN outperforms traditional tensor nuclear norm when they are used to approximate the tensor average rank. Based on the proposed p-TNN, we design an LRTC model to obtain an underlying tensor from its partial observations, which provides an upper bound for recovery error. In addition, we introduce an algorithm to solve the nonconvex optimization problem that originates in our developed model and accelerate this algorithm using an adaptive momentum scheme. Theoretical analyses indicate that our algorithm enjoys a globally geometric convergence rate under the smoothness assumption. Numerical experiments conducted on both synthetic and real-world data sets verify our method and demonstrate the superiority of our proposed p-TNN in solving LRTC problems over several state-of-the-art methods (C) 2020 Elsevier B.V. All rights reserved.