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

A high-order tensor completion algorithm based on Fully-Connected Tensor Network weighted optimization