  Matrix completion, the problem of completing missing entries in a data matrix
with low dimensional structure (such as rank), has seen many fruitful
approaches and analyses. Tensor completion is the tensor analog, that attempts
to impute missing tensor entries from similar low-rank type assumptions. In
this paper, we study the tensor completion problem when the sampling pattern is
deterministic and possibly non-uniform. We first propose an efficient weighted
HOSVD algorithm for recovery of the underlying low-rank tensor from noisy
observations and then derive the error bounds under a properly weighted metric.
Additionally, the efficiency and accuracy of our algorithm are both tested
using synthetic and real datasets in numerical simulations.
