Robust tensor completion using transformed tensor singular value decomposition

Song, Guang-Jing; Ng, Michael K.; Zhang, Xiongjun

doi:10.1002/nla.2299

Cited by 143 publications

(93 citation statements)

References 54 publications

(103 reference statements)

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“…It is also interesting to extend the Fourier transform to the wavelet transform or cosine transform (cf. [55]) for t-product in the corrected model. We use dom(f ) to denote the effective domain of f , i.e., dom(f ) = {x ∈ C : f (x) < +∞}.…”

Section: Hyperspectral Datamentioning

confidence: 99%

A Corrected Tensor Nuclear Norm Minimization Method for Noisy Low-Rank Tensor Completion

Zhang

Ng²

2019

SIAM J. Imaging Sci.

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In this paper, we study the problem of low-rank tensor recovery from limited sampling with noisy observations for third-order tensors. A tensor nuclear norm method based on a convex relaxation of the tubal rank of a tensor has been used and studied for tensor completion. In this paper, we propose to incorporate a corrected term in the tensor nuclear norm method for tensor completion. Theoretically, we provide a nonasymptotic error bound of the corrected tensor nuclear norm model for low-rank tensor completion. Moreover, we develop and establish the convergence of a symmetric Gauss-Seidel based multiblock alternating direction method of multipliers to solve the proposed correction model. Extensive numerical examples on both synthetic and real-world data are presented to validate the superiority of the proposed model over several state-of-the-art methods.

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Section: Hyperspectral Datamentioning

confidence: 99%

A Corrected Tensor Nuclear Norm Minimization Method for Noisy Low-Rank Tensor Completion

Zhang

Ng²

2019

SIAM J. Imaging Sci.

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“…Lemma 1. (Song et al, 2020) For any tensor Z ∈ R M ×I×J , suppose that Φ ∈ R J×J is a unitary transform matrix, and the SVD of the unitary transformed matrix Φ j [Z] (i.e., the jth frontal slice of the unitary transformed tensor Φ…”

Section: Computing the Variable Xmentioning

confidence: 99%

A nonconvex low-rank tensor completion model for spatiotemporal traffic data imputation

Chen¹,

Yang²,

Sun³

2020

Transportation Research Part C: Emerging Technologies

130

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Missing value problem in spatiotemporal traffic data has long been a challenging topic, in particular for largescale and high-dimensional data with complex missing mechanisms and diverse degrees of missingness. Recent studies based on tensor nuclear norm have demonstrated the superiority of tensor learning in imputation tasks by effectively characterizing the complex correlations/dependencies in spatiotemporal data. However, despite the promising results, these approaches do not scale well to large tensors. In this paper, we focus on addressing the missing data imputation problem for large-scale spatiotemporal traffic data. To achieve both high accuracy and efficiency, we develop a scalable autoregressive tensor learning model-Low-Tubal-Rank Autoregressive Tensor Completion (LATC-Tubal)-based on the existing framework of Low-Rank Autoregressive Tensor Completion (LATC by Chen and Sun (2020)), which is well-suited for spatiotemporal traffic data that characterized by multidimensional structure of location× time of day × day. In particular, the proposed LATC-Tubal model involves a scalable tensor nuclear norm minimization scheme by integrating linear unitary transformation. Therefore, the tensor nuclear norm minimization can be solved by singular value thresholding on the transformed matrix of each day while the day-today correlation can be effectively preserved by the unitary transform matrix. Before setting up the experiment, we consider two large-scale 5-minute traffic speed data sets collected by the California PeMS system with 11160 sensors: 1) PeMS-4W covers the data over 4 weeks (i.e., 288 × 28 time points), and 2) PeMS-8W covers the data over 8 weeks (i.e., 288 × 56 time points). We compare LATC-Tubal with state-of-the-art baseline models, and find that LATC-Tubal can achieve competitively accuracy with a significantly lower computational cost. In addition, the LATC-Tubal will also benefit other tasks in modeling large-scale spatiotemporal traffic data, such as network-level traffic forecasting.

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“…Different from using DFT matrix to define t-product and t-SVD in [35], we develop a novel tensor t-SVD based on orthogonal transformation [36], [37].…”

Section: A Framework Of the T-svd With Orthogonal Transformationmentioning

confidence: 99%

T-Hy-Demosaicing: Hyperspectral Reconstruction Via Tensor Subspace Representation Under Orthogonal Transformation

Huang

Lin

et al. 2021

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

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This paper aims to solve the problem of the hyperspectral imagery (HSI) demosaicing under a novel subsampling hyperspectral sensing strategy. The existing method utilizes the periodic structure of sub-sampling to estimate a fixed subspace in matrix form from the measurement result, which reduces the representation ability of the subspace in iterations and destroys the intrinsic structure of the tensor. To overcome these drawbacks, we propose a tensor-based HSI demosaicing (T-Hydemosaicing) model with tensor subspace representation, which takes the low-tubal-rankness and the nonlocal self-similarity into account. In particular, we suggest a tensor singular value decomposition based on orthogonal transformation (Tran-based t-SVD) to learn the tensor subspace that possesses a more powerful representation ability. In addition, we develop an effective algorithm to solve the proposed non-convex model under the framework of the proximal alternating minimization (PAM) algorithm. Experiments conducted on simulated datasets illustrate that the proposed method outperforms other comparative methods in both visual and quantitative terms.

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Robust tensor completion using transformed tensor singular value decomposition

Cited by 143 publications

References 54 publications

A Corrected Tensor Nuclear Norm Minimization Method for Noisy Low-Rank Tensor Completion

A Corrected Tensor Nuclear Norm Minimization Method for Noisy Low-Rank Tensor Completion

A nonconvex low-rank tensor completion model for spatiotemporal traffic data imputation

T-Hy-Demosaicing: Hyperspectral Reconstruction Via Tensor Subspace Representation Under Orthogonal Transformation

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