An efficient tensor completion method via truncated nuclear norm

Tensor completion aims to recover missing entries from partial observations for multi-dimensional data. Traditional tensor completion algorithms process the dimensional data by unfolding the tensor into matrices, which breaks the inherent correlation and dependencies in multiple channels and lead to critical information loss. In this paper, we propose a novel tensor completion model for visual multi-dimensional data completion under the tensor singular value decomposition (t-SVD) framework. In the proposed method, tensor is treated as a whole and a truncated nuclear norm regularization is employed to exploit the structural properties in a tensor and hidden information existing among the adjacent channels of a tensor. Besides, we introduce a weighted tensor to adjust the residual error of each frontal slices in consideration of their different recovery statistics. It does enhance the sparsity of all unfoldings of the tensor and accelerates the convergence of the proposed method. Experimental results on various visual datasets demonstrate the promising performance of the proposed method in comparison with the state-of-the-art tensor completion methods.