  Robust Principal Component Analysis (RPCA) aims at recovering a low-rank
subspace from grossly corrupted high-dimensional (often visual) data and is a
cornerstone in many machine learning and computer vision applications. Even
though RPCA has been shown to be very successful in solving many rank
minimisation problems, there are still cases where degenerate or suboptimal
solutions are obtained. This is likely to be remedied by taking into account of
domain-dependent prior knowledge. In this paper, we propose two models for the
RPCA problem with the aid of side information on the low-rank structure of the
data. The versatility of the proposed methods is demonstrated by applying them
to four applications, namely background subtraction, facial image denoising,
face and facial expression recognition. Experimental results on synthetic and
five real world datasets indicate the robustness and effectiveness of the
proposed methods on these application domains, largely outperforming six
previous approaches.
