  Robust principal component analysis (RPCA) is a widely used tool for
dimension reduction. In this work, we propose a novel non-convex algorithm,
coined Iterated Robust CUR (IRCUR), for solving RPCA problems, which
dramatically improves the computational efficiency in comparison with the
existing algorithms. IRCUR achieves this acceleration by employing CUR
decomposition when updating the low rank component, which allows us to obtain
an accurate low rank approximation via only three small submatrices.
Consequently, IRCUR is able to process only the small submatrices and avoid
expensive computing on the full matrix through the entire algorithm. Numerical
experiments establish the computational advantage of IRCUR over the
state-of-art algorithms on both synthetic and real-world datasets.
