Low-n-rank tensor recovery based on multi-linear augmented Lagrange multiplier method

The problem of recovering data in multi-way arrays (i.e., tensors) arises in many fields such as image processing and computer vision, etc. In this paper, we present a novel method based on multi-linear n-rank and ℓ0ℓ0 norm optimization for recovering a low-n-rank tensor with an unknown fraction of its elements being arbitrarily corrupted. In the new method, the n-rank and ℓ0ℓ0 norm of the each mode of the given tensor are combined by weighted parameters as the objective function. In order to avoid relaxing the observed tensor into penalty terms, which may cause less accuracy problem, the minimization problem along each mode is accomplished by applying the augmented Lagrange multiplier method. In experiments, we test the influence of parameters on the results of the proposed method, and then compare with one state-of-the-art method on both simulated data and real data. Numerical results show that the method can reliably solve a wide range of problems at a speed at least several times faster than the state-of-the-art method while the results of the method are comparable to the previous method in terms of accuracy.