A Low-Rank Total-Variation Regularized Tensor Completion Algorithm

Liangchen Song, Bo Du, Lefei Zhang, Liangpei Zhang

Abstract: In this paper, we first model visual data as a tensor and then impose both low-rank and total-variation constraint to complete the tensor. More specifically, we adopt a novel tensor-tensor production framework (also known as t-product) and its theory of low-rank based completion. By using the concept of t-product, it is the first time that we extend classic Total-Variation (TV) to a t-product and $$l_{1,1,2}$$ norm based constraint on the gradient of visual data. After proposing our model, we derive a iterative solver based on alternating direction method of multipliers (ADMM). We show the effectiveness of our method and compare our method with state-of-art algorithms in the experimental section.