Robust Low-tubal-rank Tensor Recovery from Binary Measurements

Hou, Jingyao; Zhang, Feng; Qiu, Haiquan; Wang, Jianjun; Wang, Yao; Meng, Deyu

doi:10.1109/tpami.2021.3063527

Cited by 18 publications

(9 citation statements)

References 54 publications

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“…Wang et al [42] defined the generalized tensor Dantzig selector to recover a low-tubal-rank tensor from noisy linear measurements. Hou et al [43] studied low-tubal-rank tensor recovery from binary measurements. Jiang [44] provided convex method for low-tubal-rank tensor completion with provable theoretical guarantee.…”

Section: B Related Workmentioning

confidence: 99%

Low-Rank Tensor Completion Based on Self-Adaptive Learnable Transforms

Gao

Fan

et al. 2024

IEEE Trans. Neural Netw. Learning Syst.

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Section: B Related Workmentioning

confidence: 99%

Low-Rank Tensor Completion Based on Self-Adaptive Learnable Transforms

Gao

Fan

et al. 2024

IEEE Trans. Neural Netw. Learning Syst.

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“…Then, a new form of TNN was proposed with the tightest convex envelope property and investigated in several tensor recovery problems [16], [47]. Recently, substantial investigations on t-SVD based tensorrelated problems have been constructed, such as [17], [18], [48]- [51]. Although these methods have attracted much attention, they cannot be applied to tensors of arbitrary order directly.…”

Section: Low-rank Tensor Recoverymentioning

confidence: 99%

Guaranteed Tensor Recovery Fused Low-rankness and Smoothness

Wang¹,

Peng²,

Qin³

et al. 2023

Preprint

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Vast visual data like multi-spectral images and multi-frame videos are essentially with the tensor format. However, due to the defects of signal acquisition equipments, the practically collected tensor data are always with evident degradations like corruptions or missing values. The tensor data recovery task has thus attracted much research attention in recent years. Solving such an ill-posed problem generally requires to explore intrinsic prior structures underlying tensor data, and formulate them as certain forms of regularization terms for guiding a sound estimate of the restored tensor. Recent research have made significant progress by adopting two insightful tensor priors, i.e., global low-rankness (L) and local smoothness (S) across different tensor modes, which are always encoded as a sum of two separate regularization terms into the recovery models. However, unlike the primary theoretical developments on low-rank tensor recovery, these joint "L+S" models have no theoretical exact-recovery guarantees yet, making the methods lack reliability in real practice. To this crucial issue, in this work, we build a unique regularization term, which essentially encodes both L and S priors of a tensor simultaneously. Especially, by equipping this single regularizer into the recovery models, we can rigorously prove the exact recovery guarantees for two typical tensor recovery tasks, i.e., tensor completion (TC) and tensor robust principal component analysis (TRPCA). To the best of our knowledge, this should be the first exact-recovery results among all related "L+S" methods for tensor recovery. We further propose ADMM algorithms for solving the proposed models, and prove their fine convergence properties. Significant recovery accuracy improvements over many other SOTA methods in several TC and TRPCA tasks with various kinds of visual tensor data are observed in extensive experiments. Typically, our method achieves a workable performance when the missing rate is extremely large, e.g., 99.5%, for the color image inpainting task, while all its peers totally fail in such challenging case. Source code is released at https://github.com/wanghailin97.

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“…The constraint also provides with theoretical continence in excluding the "spiky" tensors while controlling the identifiability of L p . Similar "non-spiky" constraints are also considered in related work [6,16,30].…”

Section: Noisy Tensor Completionmentioning

confidence: 99%

“…As has been discussed in [7] from a signal processing standpoint, the above exampled rank functions are defined in the original domain of the tensor signal and may thus be insufficient to model lowrankness in the spectral domain. The recently proposed tensor low-tubal-rankness [14] within the algebraic framework of tensor Singular Value Decomposition (t-SVD) [15] gives a kind of complement to it by exploiting low-rankness in the spectral domain defined via Discrete Fourier Transform (DFT), and has witnessed significant performance improvements in comparison with the original domain-based low-rankness for tensor recovery [6,16,17].…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Norm for Guaranteed Tensor Recovery

et al. 2022

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Benefiting from the superiority of tensor Singular Value Decomposition (t-SVD) in excavating low-rankness in the spectral domain over other tensor decompositions (like Tucker decomposition), t-SVD-based tensor learning has shown promising performance and become an emerging research topic in computer vision and machine learning very recently. However, focusing on modeling spectral low-rankness, the t-SVD-based models may be insufficient to exploit low-rankness in the original domain, leading to limited performance while learning from tensor data (like videos) that are low-rank in both original and spectral domains. To this point, we define a hybrid tensor norm dubbed the “Tubal + Tucker” Nuclear Norm (T2NN) as the sum of two tensor norms, respectively, induced by t-SVD and Tucker decomposition to simultaneously impose low-rankness in both spectral and original domains. We further utilize the new norm for tensor recovery from linear observations by formulating a penalized least squares estimator. The statistical performance of the proposed estimator is then analyzed by establishing upper bounds on the estimation error in both deterministic and non-asymptotic manners. We also develop an efficient algorithm within the framework of Alternating Direction Method of Multipliers (ADMM). Experimental results on both synthetic and real datasets show the effectiveness of the proposed model.

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Robust Low-tubal-rank Tensor Recovery from Binary Measurements

Cited by 18 publications

References 54 publications

Low-Rank Tensor Completion Based on Self-Adaptive Learnable Transforms

Low-Rank Tensor Completion Based on Self-Adaptive Learnable Transforms

Guaranteed Tensor Recovery Fused Low-rankness and Smoothness

A Hybrid Norm for Guaranteed Tensor Recovery

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