Tensor Completion using Kronecker Rank-1 Tensor Train with Application to Visual Data Inpainting

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)47804-47814
Journal / PublicationIEEE Access
Online published20 Aug 2018
Publication statusPublished - 2018


The problem of data reconstruction with partly sampled elements under a tensor structure, which is referred to as tensor completion, is addressed in this work. 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.

Research Area(s)

  • Image Reconstruction, Kronecker Rank-1 Decomposition, Multidimensional Signal Processing, Tensor Completion, Tensor Train