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As a convex surrogate of tensor multi rank, recently the tensor nuclear norm (TNN) obtains promising results in the tensor completion. However, only considering the low-tubal-rank prior is not enough for recovering the target tensor, especially when the ratio of available elements is extremely low. To address this problem, we suggest a novel low-rank tensor completion model by exploiting both low-tubal-rankness and smoothness. Especially, motivated by the capability of framelet preserving details, we characterize the spatial smoothness by framelet regularization and the smoothness of the third mode by total variation (TV) regularization. The resulting convex optimization problem is efficiently tackled by a carefully designed alternating direction method of multipliers (ADMM) algorithm. Extensive numerical results including color images, videos, and fluorescence microscope images validate the superiority of our method over the competing methods.

Low-Rank Tensor Completion via Tensor Nuclear Norm With Hybrid Smooth Regularization