Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank Approximation

doi:10.1109/TIP.2024.3385284

Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank Approximation

2024-01-01

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DOI：10.1109/TIP.2024.3385284

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Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD based low-rank approximation, which suffers from high computational costs when dealing with large-scale tensor data. Moreover, most of them are only applicable to third-order tensors. Against these issues, in this article, two efficient low-rank tensor approximation approaches fusing random projection techniques are first devised under the order-d ( d >= 3 ) T-SVD framework. Theoretical results on error bounds for the proposed randomized algorithms are provided. On this basis, we then further investigate the robust high-order tensor completion problem, in which a double nonconvex model along with its corresponding fast optimization algorithms with convergence guarantees are developed. Experimental results on large-scale synthetic and real tensor data illustrate that the proposed method outperforms other state-of-the-art approaches in terms of both computational efficiency and estimated precision.

Keywords:

High-order T-SVD framework

robust high-order tensor completion

randomized low-rank tensor approximation

nonconvex regularizers

ADMM algorithm

Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank Approximation

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