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Fast tensor robust principal component analysis with estimated multi-rank and Riemannian optimization

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Abstract

Motivated by the fact that tensor robust principal component analysis (TRPCA) and its variants do not utilize the actual rank value, which limits the recovery performance, and their computational costs are always monumental for large-scale tensor recovery, a fast TRPCA is proposed to recover the low-rank tensor and sparse tensor by estimating the multi-rank vector and adopting Riemannian optimization strategy in this paper. Specifically, a fast multi-rank estimation of low-rank tensor is proposed by modifying the Gershgorin disk theorem-based matrix rank estimation. An innovative TRPCA with Estimated Multi-Rank (TRPCA-EMR) is proposed to eliminate hyperparameter tuning by imposing strict multi-rank equality constraints. Additionally, Riemannian optimization is employed to project each frontal slice of the tensor in Fourier domain onto a low multi-rank manifold in efficiently coping with tensor Singular Value Decomposition (t-SVD) and reduce computational complexity. Experimental results on synthetic and real-world tensor datasets demonstrate TRPCA-EMR’s superior efficiency and effectiveness compared to existing methods, confirming its potential for practical applications and reassuring its reliability.

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Data Availability Statement

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

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Acknowledgements

The authors would like to express their sincere gratitude to the Editor and the anonymous reviewers for their invaluable comments and suggestions, which have significantly enhanced the quality and clarity of this paper. Their insightful feedback has been instrumental in refining our research and presenting it more effectively.

Funding

The research leading to these results received funding from the National Nature Science Foundation of China (Grant No.61371190) and the National Nature Science Foundation of China Essential project (Grant No.U2033218).

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Authors and Affiliations

Authors

Contributions

Qile Zhu: Conceptualization, Methodology, Validation, Software, Writing - original draft. Shiqian Wu: Formal analysis, Validation, Writing - review & editing. Shun Fang: Writing - review & editing. Qi Wu: Writing - review & editing. Shoulie Xie: Conceptualization, Methodology, Writing - review & editing. Sos Agaian: Supervision, writing - review & editing.

Corresponding author

Correspondence to Shiqian Wu.

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Zhu, Q., Wu, S., Fang, S. et al. Fast tensor robust principal component analysis with estimated multi-rank and Riemannian optimization. Appl Intell 55, 52 (2025). https://doi.org/10.1007/s10489-024-05899-9

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