Randomized sampling techniques based low-tubal-rank plus sparse tensor recovery

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Recently, tensor robust principal component analysis (TRPCA) based on the tensor singular value decomposition (t-SVD) framework has gained considerable attention owing to its ability to decompose a data tensor into a low-tubal-rank component and a sparse residual component. Although the tensor principal component pursuit (TPCP) program is a powerful and foremost approach for solving the TRPCA problem, it utilizes all the data to extract the intrinsic component, which causes it to be constrained by the scale of the data and makes it unsuitable for high-dimensional settings in big data applications. In this paper, using randomized sampling techniques, we propose a randomized optimization algorithm with lower computational complexity that transforms a large-scale tensor decomposition problem into two low-dimensional column/row subspace pursuit problems. In addition, the exact recovery guarantee of the proposed method is established. The obtained results suggest that the sufficient number of randomly selected columns/rows grows linearly with the changes in the rank and the coherency factor of the low-tubal-rank component. Furthermore, experimental results show that the proposed approach outperforms the full-scale TPCP in terms of decomposition efficiency on synthetic data and real color video data.