Matrix and Tensor Completion in Multiway Delay Embedded Space Using Tensor Train, With Application to Signal Reconstruction

Abstract

In this paper, the problem of time series reconstruction in a multiway delay embedded space using Tensor Train decomposition is addressed. A new algorithm has been developed in which an incomplete signal is first transformed to a Hankel matrix and in the next step to a higher order tensor using extended Multiway Delay embedded Transform. Then, the resulting higher order tensor is completed using low rank Tensor Train decomposition. Comparing to previous Hankelization approaches, in the proposed approach, blocks of elements are used for Hankelization instead of individual elements, which results in producing a higher order tensor. Simulation results confirm the effectiveness and high performance of the proposed completion approach. Although in this paper we focus on single time series, our method can be straightforwardly extended to reconstruction of multivariate time series, color images and videos.