  Tensor robust principal component analysis (TRPCA) is a fundamental model in
machine learning and computer vision. Recently, tensor train (TT) decomposition
has been verified effective to capture the global low-rank correlation for
tensor recovery tasks. However, due to the large-scale tensor data in
real-world applications, previous TRPCA models often suffer from high
computational complexity. In this letter, we propose an efficient TRPCA under
hybrid model of Tucker and TT. Specifically, in theory we reveal that TT
nuclear norm (TTNN) of the original big tensor can be equivalently converted to
that of a much smaller tensor via a Tucker compression format, thereby
significantly reducing the computational cost of singular value decomposition
(SVD). Numerical experiments on both synthetic and real-world tensor data
verify the superiority of the proposed model.
