TR-STF: a fast and accurate tensor ring decomposition algorithm via defined scaled tri-factorization

Xu, Ting; Huang, Ting‐Zhu; Deng, Liang-Jian; Dou, Hong-Xia; Yokoya, Naoto

doi:10.1007/s40314-023-02368-w

Comp. Appl. Math.

2023

DOI: 10.1007/s40314-023-02368-w

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TR-STF: a fast and accurate tensor ring decomposition algorithm via defined scaled tri-factorization

Ting Xu

Ting‐Zhu Huang

Liang-Jian Deng

et al.

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2024

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Cited by 2 publications

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“…This definition is in strong alignment with the format of Tucker decomposition. However, the calculation of the CP rank is NP-hard, and the Tucker rank inevitably destroys the internal structure of the tensor [49,50].…”

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confidence: 99%

A novel $ \ell_{0} $ minimization framework of tensor tubal rank and its multi-dimensional image completion application

Xiao,

Huang,

Deng

et al. 2024

IPI

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Recently, minimizing the tensor tubal rank based on the tensor singular value decomposition (t-SVD) has attracted significant attention in the tensor completion task. The widely-used solutions of tensor-tubal-rank minimization rely upon various convex and nonconvex surrogates of the tensor rank. However, these tensor rank surrogates usually lead to inaccurate descriptions of the tensor rank. To mitigate the limitation, we propose an innovative 0 minimization framework with guaranteed convergence to provide a novel paradigm for minimization of the tensor rank. To demonstrate the effectiveness of our framework, we develop a new tensor completion model employing a tensor adaptive sparsity-deduced rank (TASR). Subsequently, we formulate an algorithm rooted in the proposed 0 minimization framework to address this model effectively. Experimental results on multi-dimensional image data demonstrate that our method is superior to several state-of-the-art approaches. The code is accessible at https://github.com/Jin-liangXiao/L0-TC.

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confidence: 99%

A novel $ \ell_{0} $ minimization framework of tensor tubal rank and its multi-dimensional image completion application

Xiao,

Huang,

Deng

et al. 2024

IPI

Self Cite

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A Coupled Tensor Double-Factor Method for Hyperspectral and Multispectral Image Fusion

Xu,

Huang,

Deng

et al. 2024

IEEE Trans. Geosci. Remote Sensing

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TR-STF: a fast and accurate tensor ring decomposition algorithm via defined scaled tri-factorization

Cited by 2 publications

References 55 publications

A novel $ \ell_{0} $ minimization framework of tensor tubal rank and its multi-dimensional image completion application

A novel $ \ell_{0} $ minimization framework of tensor tubal rank and its multi-dimensional image completion application

A Coupled Tensor Double-Factor Method for Hyperspectral and Multispectral Image Fusion

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