Tensor Completion using Low-Rank Tensor Train Decomposition by Riemannian optimization

Tensor completion, which recovers missing entries of multiway data, plays an important role in many applications such as image processing, computer vision, machine learning, et al. There into, most of the current methods exploit this technology for image completion applications based on the tensor train (TT) decomposition, which is able to capture hidden information from tensors benefit by its well-balanced multiple matricization scheme. In order to seek a highly accurate solution comparing with traditional linear TT estimation, in this paper, we use Riemannian optimization techniques on TT manifolds to estimate images to be completed. This approach transforms the constrained linear optimization problem in Euclidean space into an unconstrained nonlinear optimization problem in Riemannian manifolds. Experiment results for color images completion show the clear advantage of our method over existed methods.