  In low-rank tensor completion tasks, due to the underlying multiple
large-scale singular value decomposition (SVD) operations and rank selection
problem of the traditional methods, they suffer from high computational cost
and high sensitivity of model complexity. In this paper, taking advantages of
high compressibility of the recently proposed tensor ring (TR) decomposition,
we propose a new model for tensor completion problem. This is achieved through
introducing convex surrogates of tensor low-rank assumption on latent tensor
ring factors, which makes it possible for the Schatten norm regularization
based models to be solved at much smaller scale. We propose two algorithms
which apply different structured Schatten norms on tensor ring factors
respectively. By the alternating direction method of multipliers (ADMM) scheme,
the tensor ring factors and the predicted tensor can be optimized
simultaneously. The experiments on synthetic data and real-world data show the
high performance and efficiency of the proposed approach.
