  In this paper, we aim at the completion problem of high order tensor data
with missing entries. The existing tensor factorization and completion methods
suffer from the curse of dimensionality when the order of tensor N>>3. To
overcome this problem, we propose an efficient algorithm called TT-WOPT
(Tensor-train Weighted OPTimization) to find the latent core tensors of tensor
data and recover the missing entries. Tensor-train decomposition, which has the
powerful representation ability with linear scalability to tensor order, is
employed in our algorithm. The experimental results on synthetic data and
natural image completion demonstrate that our method significantly outperforms
the other related methods. Especially when the missing rate of data is very
high, e.g., 85% to 99%, our algorithm can achieve much better performance than
other state-of-the-art algorithms.
