Tensor Completion Using Kronecker Rank-1 Tensor Train With Application to Visual Data Inpainting

IEEE Access

Hing Cheung So¹  Weize Sun²  Yuan Chen³ 

[1] Department of Electronic Engineering, City University of Hong Kong, Hong Kong;Shenzhen University, Shenzhen, China;University of Science and Technology Beijing, Beijing, China;

关键词: Image reconstruction;    multidimensional signal processing;    tensor completion;    tensor train;    Kronecker rank-1 decomposition;   

DOI  :  10.1109/ACCESS.2018.2866194

来源: DOAJ

【 摘 要 】

The problem of data reconstruction with partly sampled elements under a tensor structure, which is referred to as tensor completion, is addressed in this paper. The properties of the rank-1 tensor train decomposition and the tensor Kronecker decomposition are introduced at first, and then the tensor Kronecker rank as well as Kronecker rank-1 tensor train decomposition are defined. The general tensor completion idea is presented following the criterion of minimizing the number of Kronecker rank-1 tensors, which is relaxed to the thresholding problem and the solution is derived. Furthermore, the number of Kronecker rank-1 tensors that the proposed algorithm can retrieve and its complexity order are analyzed. Computer simulations are carried out on real visual data sets and demonstrate that our method yields a superior performance over the state-of-the-art approaches in terms of recovery accuracy and/or computational complexity.

【 授权许可】

Unknown