  In recent years, there have been an increasing number of applications of
tensor completion based on the tensor train (TT) format because of its
efficiency and effectiveness in dealing with higher-order tensor data. However,
existing tensor completion methods using TT decomposition have two obvious
drawbacks. One is that they only consider mode weights according to the degree
of mode balance, even though some elements are recovered better in an
unbalanced mode. The other is that serious blocking artifacts appear when the
missing element rate is relatively large. To remedy such two issues, in this
work, we propose a novel tensor completion approach via the element-wise
weighted technique. Accordingly, a novel formulation for tensor completion and
an effective optimization algorithm, called as tensor completion by parallel
weighted matrix factorization via tensor train (TWMac-TT), is proposed. In
addition, we specifically consider the recovery quality of edge elements from
adjacent blocks. Different from traditional reshaping and ket augmentation, we
utilize a new tensor augmentation technique called overlapping ket
augmentation, which can further avoid blocking artifacts. We then conduct
extensive performance evaluations on synthetic data and several real image data
sets. Our experimental results demonstrate that the proposed algorithm TWMac-TT
outperforms several other competing tensor completion methods.
