鲁棒张量主成分分析的非凸框架
The Nonconvex Framework for Robust Tensor Principal Component Analysis
摘要: 非凸鲁棒张量主成分分析问题包括从被噪声破坏的张量中恢复低秩和稀疏部分，这在广泛的实际应用中引起了极大的关注。然而，现有的非凸方法面临许多问题，其中最重要的两个问题是对特定非凸函数的限制和低秩部分的信息损失。在本文，我们提出了一种广义非凸鲁棒张量主成分分析模型(N-RTPCA)，其中包括一些最常用的非凸函数。并且提出了一个非凸ADMM算法来求解广义非凸鲁棒张量主成分分析模型(N-RTPCA)。最后，实验部分通过模拟实验和真实图片的实验验证了所提方法的优越性。
Abstract: The problem of nonconvex robust tensor principal component analysis, which consists of recovering the low-rank part and sparse part of a tensor corrupted by noise, has attracted great attention in a wide range of practical applications. However, existing nonconvex methods face many problems, the two most important of which are the restriction to specific nonconvex functions and the loss of information in the low-rank part. In this paper, we propose a generalized nonconvex robust tensor principal component analysis model (N-RTPCA) which includes some of the most commonly used nonconvex functions. And a nonconvex ADMM algorithm is proposed to solve the generalized nonconvex robust tensor principal component analysis model (N-RTPCA). Finally, the experimental part verifies the superiority of the proposed method by simulation experiments and experiments on real pictures.
文章引用：唐开煜, 樊亚莉. 鲁棒张量主成分分析的非凸框架[J]. 建模与仿真, 2024, 13(4): 4171-4179. https://doi.org/10.12677/mos.2024.134378

参考文献

[1] Kolda, T.G. and Bader, B.W. (2009) Tensor Decompositions and Applications. SIAM Review, 51, 455-500. [Google Scholar] [CrossRef] 
[2] Lu, C., Feng, J., Chen, Y., Liu, W., Lin, Z. and Yan, S. (2016). Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization. 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, 27-30 June 2016, 5249-5257.[CrossRef] 
[3] Chen, L., Liu, Y. and Zhu, C. (2017). Iterative Block Tensor Singular Value Thresholding for Extraction of Lowrank Component of Image Data. 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, 5-9 March 2017, 1862-1866.[CrossRef] 
[4] Kilmer, M.E. and Martin, C.D. (2011) Factorization Strategies for Third-Order Tensors. Linear Algebra and Its Applications, 435, 641-658. [Google Scholar] [CrossRef] 
[5] Kilmer, M.E., Braman, K., Hao, N. and Hoover, R.C. (2013) Third-Order Tensors as Operators on Matrices: A Theoretical and Computational Framework with Applications in Imaging. SIAM Journal on Matrix Analysis and Applications, 34, 148-172. [Google Scholar] [CrossRef] 
[6] Lu, C., Feng, J., Chen, Y., Liu, W., Lin, Z. and Yan, S. (2020) Tensor Robust Principal Component Analysis with a New Tensor Nuclear Norm. IEEE Transactions on Pattern Analysis and Machine Intelligence, 42, 925-938. [Google Scholar] [CrossRef] [PubMed]
[7] Lu, C., Feng, J., Yan, S. and Lin, Z. (2018) A Unified Alternating Direction Method of Multipliers by Majorization Minimization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 40, 527-541. [Google Scholar] [CrossRef] [PubMed]
[8] Zhang, F., Wang, J., Wang, W. and Xu, C. (2021) Low-Tubal-Rank Plus Sparse Tensor Recovery with Prior Subspace Information. IEEE Transactions on Pattern Analysis and Machine Intelligence, 43, 3492-3507. [Google Scholar] [CrossRef] [PubMed]
[9] Zhou, P., Lu, C., Feng, J., Lin, Z. and Yan, S. (2021) Tensor Low-Rank Representation for Data Recovery and Clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 43, 1718-1732. [Google Scholar] [CrossRef] [PubMed]
[10] Liu, Y., Chen, L. and Zhu, C. (2018) Improved Robust Tensor Principal Component Analysis via Low-Rank Core Matrix. IEEE Journal of Selected Topics in Signal Processing, 12, 1378-1389. [Google Scholar] [CrossRef] 
[11] Shi, Q., Cheung, Y. and Lou, J. (2022) Robust Tensor SVD and Recovery with Rank Estimation. IEEE Transactions on Cybernetics, 52, 10667-10682. [Google Scholar] [CrossRef] [PubMed]
[12] Xu, W., Zhao, X., Ji, T., Miao, J., Ma, T., Wang, S., et al. (2019) Laplace Function Based Nonconvex Surrogate for Low-Rank Tensor Completion. Signal Processing: Image Communication, 73, 62-69. [Google Scholar] [CrossRef] 
[13] Sun, X., Zhang, X., Xu, C., Xiao, M. and Tang, Y. (2023) Tensorial Multiview Representation for Saliency Detection via Nonconvex Approach. IEEE Transactions on Cybernetics, 53, 1816-1829. [Google Scholar] [CrossRef] [PubMed]
[14] Wang, H., Zhang, F., Wang, J., Huang, T., Huang, J. and Liu, X. (2022) Generalized Nonconvex Approach for Low-Tubal-Rank Tensor Recovery. IEEE Transactions on Neural Networks and Learning Systems, 33, 3305-3319. [Google Scholar] [CrossRef] [PubMed]
[15] Cai, S., Luo, Q., Yang, M., Li, W. and Xiao, M. (2019) Tensor Robust Principal Component Analysis via Non-Convex Low Rank Approximation. Applied Sciences, 9, Article 1411. [Google Scholar] [CrossRef] 
[16] Li, T. and Ma, J. (2021). T-SVD Based Non-Convex Tensor Completion and Robust Principal Component Analysis. 2020 25th International Conference on Pattern Recognition (ICPR), Milan, 10-15 January 2021, 6980-6987.[CrossRef] 
[17] Martin D, Fowlkes C, Tal D, et al. (2001) A Database of Human Segmented Natural Images and Its Application to Evaluating Segmentation Algorithms and Measuring Ecological Statistics. Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001, Vancouver, 7-14 July 2001, 416-423. [Google Scholar] [CrossRef] 

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