Robust CUR Decomposition: Theory and Imaging Applications*

This paper considers the use of robust principal component analysis (RPCA) in a CUR decomposition framework and applications thereof. Our main algorithms produce a robust version of columnrow factorizations of matrices D = L + S, where L is low-rank and S contains sparse outliers. These methods yield interpretable factorizations at low computational cost and provide new CUR decompositions that are robust to sparse outliers, in contrast to previous methods. We consider two key imaging applications of RPCA: video foreground-background separation and face modeling. This paper examines the qualitative behavior of our robust CUR decompositions on the benchmark videos and face datasets and finds that our method works as well as standard RPCA while being significantly faster. Additionally, we consider hybrid randomized and deterministic sampling methods which produce a compact CUR decomposition of a given matrix and apply this to video sequences to produce canonical frames thereof.