Tensor Recovery via 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 ℓ₀ 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 ℓ₀ 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. The proposed approach is evaluated both on simulated data and real world data. Experimental results show that our proposed method tends to deliver higher-quality solutions with faster convergence rate compared with previous methods.