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

Image Completion in Embedded Space Using Multistage Tensor Ring Decomposition

“…For overcoming this limitation, the acquired datasets are represented in tensor formats. Tensors are higher order arrays used in different signal processing applications such as Blind Source Separation (BSS) (Cichocki et al, 2009;Bousse et al, 2016), image in-painting/completion (Liu et al, 2012;Yokota et al, 2016;Wang et al, 2017), time series analysis (Kouchaki et al, 2014;Sedighin et al, 2020) and machine learning (Rabanser et al, 2017;Sidiropoulos et al, 2017).…”

“…Recently, a promising approach, called Hankelization, has been developed for improving the quality of tensor completion approaches (Yokota et al, 2018;Sedighin et al, 2020). Previously, Hankelization has been used as an initial step for a time series analysis algorithm, called Singular Spectrum Analysis (SSA) (Golyandina et al, 2013;Rahmani et al, 2016;Hassani et al, 2017;Kalantari et al, 2018).…”

“…In (Asante-Mensah et al, 2020), TR decomposition has been used for the completion of Hankelized images. Also in (Sedighin et al, 2020), a new approach for time series completion based on a two-stage Hankelization has been proposed. In this approach, a one way data, i.e., the time series, is first reformatted into a Hankel matrix, and then the resulting Hankel matrix is block Hankelized into a 6-th order tensor using block (patch) Hankelization.…”

“…In this approach, a one way data, i.e., the time series, is first reformatted into a Hankel matrix, and then the resulting Hankel matrix is block Hankelized into a 6-th order tensor using block (patch) Hankelization. In block Hankelization approach, in contrast to classic Hankelization methods, blocks of elements are Hankelized instead of individual elements (Sedighin et al, 2020).…”

“…In this paper, we mainly focus on image completion. Using the block Hankelization approach of (Sedighin et al, 2020), the original incomplete tensor (image) is first transformed into a higher order 7-D tensor. Then a TR decomposition has been applied for image completion.…”