Abstract
Tensor Completion is an important problem in big data processing. Usually, data acquired from different aspects of a multimodal phenomenon or different sensors are incomplete due to different reasons such as noise, low sampling rate or human mistake. In this situation, recovering the missing or uncertain elements of the incomplete dataset is an important step for efficient data processing. In this paper, a new completion approach using Tensor Ring (TR) decomposition in the embedded space has been proposed. In the proposed approach, the incomplete data tensor is first transformed into a higher order tensor using the block Hankelization method. Then the higher order tensor is completed using TR decomposition with rank incremental and multistage strategy. Simulation results show the effectiveness of the proposed approach compared to the state of the art completion algorithms, especially for very high missing ratios and noisy cases.
Highlights
Joint analysis of datasets recorded by different sensors is an effective approach for investigating a physical phenomenon
Tensor Train (TT) rank minimization has been used in many of tensor completion algorithms. These algorithms are basically categorized as the rank minimization based approaches, since they are using TT rank which is closely related to TT decomposition, we have briefly reviewed them
In (Yokota et al, 2018), Hankelization is performed by multiplying a special matrix, called duplication matrix, by each of the modes of the original tensor followed by a tensorization step
Summary
Joint analysis of datasets recorded by different sensors is an effective approach for investigating a physical phenomenon. Due to the Hankel structure, it is expected that the resulting higher order tensor provided by the Hankelization is low rank This low-rankness in addition to a rank incremental strategy for Tucker model has been used for tensor completion in (Yokota et al, 2018). To best of our knowledge, this is the first time of using multistage strategy for image completion along with adaptive TR decomposition This is the main difference of the proposed approach with the simulation presented in (Sedighin et al, 2021).
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