Tensor RPCA by Bayesian CP Factorization with Complex Noise

The RPCA model has achieved good performances in various applications. However, two defects limit its effectiveness. Firstly, it is designed for dealing with data in matrix form, which fails to exploit the structure information of higher order tensor data in some pratical situations. Secondly, it adopts L1-norm to tackle noise part which makes it only valid for sparse noise. In this paper, we propose a tensor RPCA model based on CP decomposition and model data noise by Mixture of Gaussians (MoG). The use of tensor structure to raw data allows us to make full use of the inherent structure priors, and MoG is a general approximator to any blends of consecutive distributions, which makes our approach capable of regaining the low dimensional linear subspace from a wide range of noises or their mixture. The model is solved by a new proposed algorithm inferred under a variational Bayesian framework. The superiority of our approach over the existing state-of-the-art approaches is demonstrated by extensive experiments on both of synthetic and real data.