Robust PCA via tensor outlier pursuit

In this paper, we study robust principal component analysis on tensors, in the setting where frame-wise outliers exist. We propose a convex formulation to decompose a tensor into a low rank component and a frame-wise sparse component. Theoretically, we guarantee that exact subspace recovery and outlier identification can be achieved under mild model assumptions. Compared with entry-wise outlier pursuit and naive matricization of tensors with frame-wise outliers, our approach can handle higher ranks and proportion of outliers. Extensive numerical evaluations are provided on both synthetic and real data to support our theory.