Robust CUR Decomposition: Theory and Imaging Applications
This work provides a faster and robust matrix factorization method for imaging applications, particularly beneficial for tasks like video analysis and face modeling where sparse outliers are common.
This paper introduces a Robust CUR decomposition method that factorizes matrices into a low-rank component and a sparse outlier component. The method is applied to video foreground-background separation and face modeling, achieving comparable performance to standard Robust PCA but with significantly faster computation.
This paper considers the use of Robust PCA in a CUR decomposition framework and applications thereof. Our main algorithms produce a robust version of column-row factorizations of matrices $\mathbf{D}=\mathbf{L}+\mathbf{S}$ where $\mathbf{L}$ is low-rank and $\mathbf{S}$ 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 Robust PCA: 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 find that our method works as well as standard Robust PCA 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.