Low-tubal-rank tensor completion via local and nonlocal knowledge

Abstract

Many previous studies have indicated that exploiting prior information about the underlying tensor data is a sound approach for completing missing or damaged entries. This prior information can be divided into three commonly used categories: low-rankness, local piecewise smoothness, and nonlocal self-similarity (NSS) priors. Although existing methods based on these priors have gained considerable attention, the majority of studies utilize only one or two of these priors, leading to inadequate extraction of structural information from tensors. To address this limitation and comprehensively depict the inherent structural information of underlying tensor data, this article develops a novel tensor completion framework that can simultaneously utilize the three abovementioned priors within a plug-and-play framework. More precisely, we adopt the tensor correlated total variation (t-CTV) norm as a robust representation for capturing the combined effects of low-rankness and local piecewise smoothness priors, eliminating the need for a trade-off parameter in the process; meanwhile, we introduce an advanced denoiser to explore the NSS prior. Furthermore, to address the presented optimization model, we design an alternating direction method of multipliers (ADMM) algorithm and innovatively provide its corresponding global convergence guarantees. Extensive numerical experiments on real tensor data, including color, medical and hyperspectral images, demonstrate that the proposed method surpasses various advanced approaches in terms of both quality metrics and visual effects.