Fast adaptive tubal rank-revealing algorithm for t-product based tensor approximation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913985710784512 |
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| author | Liu, Qiaohua Gu, Jiehui |
| author_facet | Liu, Qiaohua Gu, Jiehui |
| contents | Color images and video sequences can be modeled as three-way tensors, which admit low tubal-rank approximations via convex surrogate minimization. This optimization problem is efficiently addressed by tensor singular value thresholding (t-SVT). To mitigate the computational burden of tensor singular value decomposition (t-SVD) in each iteration, this paper introduces an adaptive randomized algorithm for tubal rank revelation in data tensors \(\mathcal{A}\). Our method selectively captures the principal information from frontal slices in the Fourier domain using a predefined threshold, obviating the need for priori tubal-rank and Fourier-domain singular values estimations while providing an explicit tensor approximation. Leveraging optimality results from matrix randomized SVD, we establish theoretical guarantees demonstrating that the proposed algorithm computes low tubal-rank approximations within constants dependent on data dimensions and the Fourier-domain singular value gap. Empirical evaluations validate its efficacy in image processing and background modeling tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08557 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fast adaptive tubal rank-revealing algorithm for t-product based tensor approximation Liu, Qiaohua Gu, Jiehui Numerical Analysis Color images and video sequences can be modeled as three-way tensors, which admit low tubal-rank approximations via convex surrogate minimization. This optimization problem is efficiently addressed by tensor singular value thresholding (t-SVT). To mitigate the computational burden of tensor singular value decomposition (t-SVD) in each iteration, this paper introduces an adaptive randomized algorithm for tubal rank revelation in data tensors \(\mathcal{A}\). Our method selectively captures the principal information from frontal slices in the Fourier domain using a predefined threshold, obviating the need for priori tubal-rank and Fourier-domain singular values estimations while providing an explicit tensor approximation. Leveraging optimality results from matrix randomized SVD, we establish theoretical guarantees demonstrating that the proposed algorithm computes low tubal-rank approximations within constants dependent on data dimensions and the Fourier-domain singular value gap. Empirical evaluations validate its efficacy in image processing and background modeling tasks. |
| title | Fast adaptive tubal rank-revealing algorithm for t-product based tensor approximation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2508.08557 |