Mixture Augmented Lagrange Multiplier Method for Tensor Recovery and Its Applications

The problem of data recovery in multiway arrays (i.e., tensors) arises in many fields such as computer vision, image processing, and traffic data analysis. In this paper, we propose a scalable and fast algorithm for recovering a low-n-rank tensor with an unknown fraction of its entries being arbitrarily corrupted. In the new algorithm, the tensor recovery problem is formulated as a mixture convex multilinear Robust Principal Component Analysis (RPCA) optimization problem by minimizing a sum of the nuclear norm and the ℓ1-norm. The problem is well structured in both the objective function and constraints. We apply augmented Lagrange multiplier method which can make use of the good structure for efficiently solving this problem. In the experiments, the algorithm is compared with the state-of-art algorithm both on synthetic data and real data including traffic data, image data, and video data