Robust Principal Component Analysis with Complex Noise

The research on robust principal component analysis (RPCA) has been attracting much attention recently. The original RPCA model assumes sparse noise, and use the L-1-norm to characterize the error term. In practice, however, the noise is much more complex and it is not appropriate to simply use a certain L-p-norm for noise modeling. We propose a generative RPCA model under the Bayesian framework by modeling data noise as a mixture of Gaussians (MoG). The MoG is a universal approximator to continuous distributions and thus our model is able to fit a wide range of noises such as Laplacian, Gaussian, sparse noises and any combinations of them. A variational Bayes algorithm is presented to infer the posterior of the proposed model. All involved parameters can be recursively updated in closed form. The advantage of our method is demonstrated by extensive experiments on synthetic data, face modeling and background subtraction.