Bayesian robust principal component analysis with structured sparse component

The robust principal component analysis (RPCA) refers to the decomposition of an observed matrix into the low-rank component and the sparse component. Conventional methods model the sparse component as pixel-wisely sparse (e.g., ℓ1-norm for the sparsity). However, in many practical scenarios, elements in the sparse part are not truly independently sparse but distributed with contiguous structures. This is the reason why representative RPCA techniques fail to work well in realistic complex situations. To solve this problem, a Bayesian framework for RPCA with structured sparse component is proposed, where both amplitude and support correlation structure are considered simultaneously in recovering the sparse component. The model learning is based on the variational Bayesian inference, which can potentially be applied to estimate the posteriors of all latent variables. Experimental results demonstrate the proposed methodology is validated on synthetic and real data.