Tensor Completion Based on Triple Tubal Nuclear Norm

Wei, Dongxu; Wang, Andong; Feng, Xiao; Wang, Boyu; Wang, Bo

doi:10.3390/a11070094

Cited by 14 publications

(6 citation statements)

References 46 publications

(88 reference statements)

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“…(1) The orientational sensitivity of * L -SVD: Despite the promising empirical performance of the * L -SVD-based estimator, a typical defect of it is the orientation sensitivity owing to low-rankness strictly defined along the tubal orientation which makes it fail to simultaneously exploit transformed low-rankness in multiple orientations [19,58]. (2) The difficulty in finding the optimal transform L(•) for * L -SVD: Although a direct use of fixed transforms (like DFT and DCT) may produce fairish empirical performance, it is still unclear how to find the best optimal transformation L(•) for any certain tensor L * when only partial and corrupted observations are available.…”

Section: Discussionmentioning

confidence: 99%

Guaranteed Robust Tensor Completion via ∗L-SVD with Applications to Remote Sensing Data

2021

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This paper conducts a rigorous analysis for the problem of robust tensor completion, which aims at recovering an unknown three-way tensor from incomplete observations corrupted by gross sparse outliers and small dense noises simultaneously due to various reasons such as sensor dead pixels, communication loss, electromagnetic interferences, cloud shadows, etc. To estimate the underlying tensor, a new penalized least squares estimator is first formulated by exploiting the low rankness of the signal tensor within the framework of tensor ∗L-Singular Value Decomposition (∗L-SVD) and leveraging the sparse structure of the outlier tensor. Then, an algorithm based on the Alternating Direction Method of Multipliers (ADMM) is designed to compute the estimator in an efficient way. Statistically, the non-asymptotic upper bound on the estimation error is established and further proved to be optimal (up to a log factor) in a minimax sense. Simulation studies on synthetic data demonstrate that the proposed error bound can predict the scaling behavior of the estimation error with problem parameters (i.e., tubal rank of the underlying tensor, sparsity of the outliers, and the number of uncorrupted observations). Both the effectiveness and efficiency of the proposed algorithm are evaluated through experiments for robust completion on seven different types of remote sensing data.

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Section: Discussionmentioning

confidence: 99%

Guaranteed Robust Tensor Completion via ∗L-SVD with Applications to Remote Sensing Data

2021

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“…It differs from SNN (Liu et al 2013) which only considers low Tucker rank. As special cases, if K = 3, OITNN-O degenerates to triple TNN (Wei et al 2018); If K = 3, (w 1 , w 3 ) → 0, then it approximates TNN.…”

Section: Lemma 1 It Holds For Any Tensormentioning

confidence: 99%

Robust Tensor Decomposition via Orientation Invariant Tubal Nuclear Norms

Wang¹,

Zhao

2020

AAAI

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Low-rank tensor recovery has been widely applied to computer vision and machine learning. Recently, tubal nuclear norm (TNN) based optimization is proposed with superior performance as compared to other tensor nuclear norms. However, one major limitation is its orientation sensitivity due to low-rankness strictly defined along tubal orientation and it cannot simultaneously model spectral low-rankness in multiple orientations. To this end, we introduce two new tensor norms called OITNN-O and OITNN-L to exploit multi-orientational spectral low-rankness for an arbitrary K-way (K ≥ 3) tensors. We further formulate two robust tensor decomposition models via the proposed norms and develop two algorithms as the solutions. Theoretically, we establish non-asymptotic error bounds which can predict the scaling behavior of the estimation error. Experiments on real-world datasets demonstrate the superiority and effectiveness of the proposed norms.

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“…Other stateof-the-art methods, i.e. FBCP [22], TMac [7], TriTNN [2], HaLTRC [34], SiLRTC-TT [35], TNN [26], TRNNM [36], FFWTensor [14], are chosen as the baseline methods of the proposed method. The performance of these methods is obtained by tuning their parameters according to the corresponding papers.…”

Section: Analysis Of Space-complexity and Time-complexitymentioning

confidence: 99%

An Efficient Tensor Completion Method Via New Latent Nuclear Norm

Sun

Qiu

et al. 2020

IEEE Access

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In tensor completion, the latent nuclear norm is commonly used to induce low-rank structure, while substantially failing to capture the global information due to the utilization of unbalanced unfolding schemes. To overcome this drawback, a new latent nuclear norm equipped with a more balanced unfolding scheme is defined for low-rank regularizer. Moreover, the new latent nuclear norm together with the Frank-Wolfe (FW) algorithm is developed as an efficient completion method by utilizing the sparsity structure of observed tensor. Specifically, both FW linear subproblem and line search only need to access the observed entries, by which we can instead maintain the sparse tensors and a set of small basis matrices during iteration. Most operations are based on sparse tensors, and the closed-form solution of FW linear subproblem can be obtained from rank-one SVD. We theoretically analyze the space-complexity and time-complexity of the proposed method, and show that it is much more efficient over other norm-based completion methods for higher-order tensors. Extensive experimental results of visual-data inpainting demonstrate that the proposed method is able to achieve state-of-the-art performance at smaller costs of time and space, which is very meaningful for the memory-limited equipment in practical applications. INDEX TERMS Tensor completion, tensor ring decomposition, tensor ring rank, latent nuclear norm, image/video inpainting.

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Tensor Completion Based on Triple Tubal Nuclear Norm

Cited by 14 publications

References 46 publications

Guaranteed Robust Tensor Completion via ∗L-SVD with Applications to Remote Sensing Data

Guaranteed Robust Tensor Completion via ∗L-SVD with Applications to Remote Sensing Data

Robust Tensor Decomposition via Orientation Invariant Tubal Nuclear Norms

An Efficient Tensor Completion Method Via New Latent Nuclear Norm

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