Robust low-rank tensor reconstruction using high-order t-SVD

Qin, Wenjin; Wang, Hailin; Zhang, Feng; Dai, Mingwei; Wang, Jianjun

doi:10.1117/1.jei.30.6.063016

Cited by 5 publications

(5 citation statements)

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“…That is, the weight values should be inversely proportional to the singular values in the transform domain. In particular, the HWTSN 1) is equivalent to the high-order tensor Schatten-p norm (HTSN) when weighting is not taken into account, 2) reduces to the high-order weighted TNN (HWTNN) [61] when p = 1, and 3) simplifies to the high-order TNN (HTNN) [58] when p = 1, and W is not considered.…”

Section: Notations and Preliminariesmentioning

confidence: 99%

“…Thus, the original components corresponding to the larger singular values will be less affected. The GTSVT operator is more flexible than the T-SVT operator proposed in [58] (shrinks all singular values with the same threshold) and the WTSVT operator proposed in [61], and provides more degree of freedom for the approximation to the original problem.…”

Section: B Hwtsn Minimization Problemmentioning

confidence: 99%

“…In this subsection, we mainly perform the efficiency/precision validation and convergence study on the synthetic high-order tensors, and also compare the obtained results of the proposed method (HWTSN+w q ) with the baseline RLRTC method induced by high-order T-SVD framework, i.e., HWTNN+ 1 [61]. Two fast versions (i.e., they incorporate the unblocked and blocked randomized strategies, respectively) of "HWTSN+w q " are called HWTSN+w q (UR) and HWTSN+w q (BR), respectively.…”

Section: A Synthetic Experimentsmentioning

confidence: 99%

“…Experiment Settings: In this subsection, we apply the proposed method (HWTSN+w q ) and its two accelerated versions to several real-world applications, and also compare it with other RLRTC approaches: SNN+ 1 [11], TRNN+ 1 [15], TTNN+ 1 [24], TSP-k+ 1 [23], LNOP [27], NRTRM [29], and HWTNN+ 1 [61]. In our experiments, we normalize the gray-scale value of the tested tensors to the interval [0, 1].…”

Section: B Real-world Applicationsmentioning

confidence: 99%

“…However, we observe that these approaches are only relevant to third-order tensors. To fix this problem, Qin et al established an order-d (d ≥ 3) T-SVD algebraic framework [58] based on a family of invertible linear transforms, and then preliminary investigated the model, algorithm, and theory for the robust high-order tensor completion (RHTC) [58]- [61]. The RHTC methods generated by other tensor factorization frameworks can be found in [11]- [19].…”

Section: Introductionmentioning

confidence: 99%

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ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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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 randomized techniques are first devised under the order-d (d ≥ 3) T-SVD framework. On this basis, we then further investigate the robust highorder tensor completion (RHTC) problem, in which a double nonconvex model along with its corresponding fast optimization algorithms with convergence guarantees are developed. To the best of our knowledge, this is the first study to incorporate the randomized low-rank approximation into the RHTC problem. Empirical studies on large-scale synthetic and real tensor data illustrate that the proposed method outperforms other state-ofthe-art approaches in terms of both computational efficiency and estimated precision.

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Section: Notations and Preliminariesmentioning

confidence: 99%

Section: B Hwtsn Minimization Problemmentioning

confidence: 99%

Section: A Synthetic Experimentsmentioning

confidence: 99%