  Tensor completion aimes at recovering missing data, and it is one of the
popular concerns in deep learning and signal processing. Among the higher-order
tensor decomposition algorithms, the recently proposed fully-connected tensor
network decomposition (FCTN) algorithm is the most advanced. In this paper, by
leveraging the superior expression of the fully-connected tensor network (FCTN)
decomposition, we propose a new tensor completion method named the fully
connected tensor network weighted optization(FCTN-WOPT). The algorithm performs
a composition of the completed tensor by initialising the factors from the FCTN
decomposition. We build a loss function with the weight tensor, the completed
tensor and the incomplete tensor together, and then update the completed tensor
using the lbfgs gradient descent algorithm to reduce the spatial memory
occupation and speed up iterations. Finally we test the completion with
synthetic data and real data (both image data and video data) and the results
show the advanced performance of our FCTN-WOPT when it is applied to
higher-order tensor completion.
