Robust Tensor Recovery using Low-Rank Tensor Ring

Robust tensor completion recoveries the low-rank and sparse parts from its partially observed entries. In this paper, we propose the robust tensor ring completion (RTRC) model and rigorously analyze its exact recovery guarantee via TR-unfolding scheme, and the result is consistent with that of matrix case. We propose the algorithms for tensor ring robust principle component analysis (TRRPCA) and RTCR using the alternating direction method of multipliers (ADMM). The numerical experiment demonstrates that the proposed method outperforms the state-of-the-art ones in terms of recovery accuracy.