Robust Principal Component Analysis with Complex Noise

The research on robust principal component analysis (RPCA) has been attracting much atten-tion recently. The original RPCA model assumes sparse noise, and use the L1-norm to characterize the error term. In practice, however, the noise is much more complex and it is not appropriate to simply use a certainLp-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 uni-versal 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 varia-tional 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 demon-strated by extensive experiments on synthetic da-ta, face modeling and background subtraction. 1.