Robust low-rank tensor completion via new regularized model with approximate SVD

Tensor recovery with tensor singular value decomposition has recently become increasingly popular in the computer vision field. One of the most important subproblem is the low-rank tensor completion with the partial and/or corrupted observations. In this paper, we propose a new low-rank tensor completion model with the robust form by minimizing the reconstruction error of approximate SVD and the γ nuclear norm of the lower triangular tensor, and then give their equivalent forms with the tensor slices in the Fourier domain. The efficient iterative algorithm is developed to solve the minimization problem, and the convergence of the algorithm is discussed. Experimental results on real-world visual data and the internet traffic data show that the proposed approaches outperform the state of the art algorithms in both (robust) recovery accuracy and computing time.