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.

提出了一种名为 RTCUR 的快速算法，用于在 Tucker 秩设置下，将给定的张量分成基础低秩分量和稀疏异常分量的大规模非凸 TRPCA 问题中，利用交替投影框架在低秩张量集和稀疏张量集之间进行投影，并利用最近开发的张量 CUR 分解大大降低了每个投影的计算复杂度，通过在合成和真实数据集上的实验，证明了 RTCUR 算法的有效性和计算优势，是一种研究 tensor robust principal component analysis 问题的有效方法。