Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruptions

SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 225-247, March 2024.
Abstract. We study the tensor robust principal component analysis (TRPCA) problem, a tensorial extension of matrix robust principal component analysis, which 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 nonconvex 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.