ENHANCING LOW-RANK TENSOR COMPLETION VIA FIRST-ORDER AND SECOND-ORDER TOTAL VARIATION REGULARIZATIONS

Recently, low-rank tensor completion (LRTC) has attracted sig-nificant 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 usu-ally 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 conver-gence 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.