Enhancing low-rank tensor completion via first-order and second-order total variation regularizations

Abstract

<p style='text-indent:20px;'>Recently, low-rank tensor completion (LRTC) has attracted significant attention since it has been applied in a wide variety of practical areas. Due to the edge-preserving and noise removal properties, total variation (TV) has been extensively used in LRTC problems. However, first-order TV usually causes unexpected staircase effects. In this paper, we focus on the LRTC problem with various degradations, which aims to recover third-order tensors from partial observations corrupted by sparse noise and Gaussian noise. We use the transformed tensor nuclear norm to explore global low-rankness, and the combination of first-order and second-order TV regularizations to alleviate the staircase effects caused by first-order TV. Based on these, we propose a first-order and second-order TV regularizations (FSTV) model. In order to solve the proposed FSTV model, a symmetric Gauss-Seidel based alternating direction method of multipliers is adopted. We also establish its global convergence under very mild conditions. Finally, extensive experiments on different video and multispectral image datasets show the superiority of the proposed method compared with several state-of-the-art methods.</p>