  We study the tensor robust principal component analysis (TRPCA) problem, a
tensorial extension of matrix robust principal component analysis (RPCA), that
aims to split the given tensor into an underlying low-rank component and a
sparse outlier component. This work proposes a fast algorithm, called Robust
Tensor CUR Decompositions (RTCUR), for large-scale non-convex TRPCA problems
under the Tucker rank setting. RTCUR is developed within a framework of
alternating projections that projects between the set of low-rank tensors and
the set of sparse tensors. We utilize the recently developed tensor CUR
decomposition to substantially reduce the computational complexity in each
projection. In addition, we develop four variants of RTCUR for different
application settings. We demonstrate the effectiveness and computational
advantages of RTCUR against state-of-the-art methods on both synthetic and
real-world datasets.
