[1]PAN Yuyan,ZHANG De,LI Zhuangju.Nonconvex TRPCA algorithm combined with low-rank pre-separation and random jitter mechanism[J].CAAI Transactions on Intelligent Systems,2025,20(4):822-837.[doi:10.11992/tis.202406003]
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Nonconvex TRPCA algorithm combined with low-rank pre-separation and random jitter mechanism

CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume: 20 Number of periods: 2025 4 Page number: 822-837 Column: 学术论文—机器学习 Public date: 2025-08-05
Title:
Nonconvex TRPCA algorithm combined with low-rank pre-separation and random jitter mechanism
Author(s):
PAN Yuyan;  ZHANG De;  LI Zhuangju
School of Electrical and Information Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
Keywords:
principal component analysis; tensor; image denoising; image processing; machine learning; computer application; signal processing; singular value decomposition
CLC:
TP391
DOI:
10.11992/tis.202406003
Abstract:
To address the issue of information extraction bias caused by uniform shrinkage of singular values in tensor robust principal component analysis (TRPCA) during low-rank structure recovery, this study considered treating singular values differently, using a nonconvex weighted tensor Schatten-p norm (0<p<1) to analyze tensor data, which reduced the penalty for singular values. In order to solve the problem of severe data damage that is difficult to recover, a low-rank pre-separation method was used to realize the pre-separation of the approximate low-rank component and the approximate sparse component. To enhance the correlation among high-order tensors while reducing the sensitivity of data to specific noise, the random jitter regularizer mechanism was proposed to optimize the selected random regions for the pre-separated components respectively, which constrained the complexity of the model by using the randomness of the noise information to regularize the algorithm. Finally, experiments were conducted on high-dimensional data recovery using different types of image datasets, including color images, MRI images, hyperspectral and multispectral images, and grayscale images. The results show that the proposed method significantly outperforms other TRPCA approaches in image recovery performance and maintains advantages even under severe data corruption. It effectively extracts principal component information while reducing dependence on specific noise patterns, demonstrating strong robustness and adaptability. This method can serve as a valuable reference for TRPCA-based image recovery applications.
References:
[1] 倪怀发, 沈肖波, 孙权森. 基于低秩分解的鲁棒典型相关分析[J]. 智能系统学报, 2017, 12(4): 491-497.
NI Huaifa, SHEN Xiaobo, SUN Quansen. Robust canonical correlation analysis based on low rank decomposition[J]. CAAI transactions on intelligent systems, 2017, 12(4): 491-497.
[2] CANDèS E J, LI Xiaodong, MA Yi, et al. Robust principal component analysis?[J]. Journal of the ACM, 2011, 58(3): 1-37.
[3] CAI Jianfeng, CANDèS E J, SHEN Zuowei. A singular value thresholding algorithm for matrix completion[J]. SIAM journal on optimization, 2010, 20(4): 1956-1982.
[4] ASANTE-MENSAH M G, PHAN A H, AHMADI-ASL S, et al. Image reconstruction using superpixel clustering and tensor completion[J]. Signal processing, 2023, 212: 109158.
[5] ZHENG Jianwei, YANG Ping, YANG Xi, et al. Truncated low-rank and total p variation constrained color image completion and its Moreau approximation algorithm[J]. IEEE transactions on image processing, 2020, 29: 7861-7874.
[6] OH T H, TAI Y W, BAZIN J C, et al. Partial sum minimization of singular values in robust PCA: algorithm and applications[J]. IEEE transactions on pattern analysis and machine intelligence, 2016, 38(4): 744-758.
[7] ZHU Lin, JIANG Xiurong, LI Jianing, et al. Motion-aware structured matrix factorization for foreground detection in complex scenes[J]. ACM transactions on multimedia computing, communications, and applications, 2020, 16(4): 1-23.
[8] ZHONG Guo, PUN C M. RPCA-induced self-representation for subspace clustering[J]. Neurocomputing, 2021, 437: 249-260.
[9] 王丽娟, 丁世飞, 夏菁. 基于多样性的多视图低秩稀疏子空间聚类算法[J]. 智能系统学报, 2022, 18(2): 399-408.
WANG Lijuan, DING Shifei, XIA Jing. Multiview low-rank sparse subspace clustering based on diversity[J]. CAAI transactions on intelligent systems, 2022, 18(2): 399-408.
[10] 吴小艺, 吴小俊. 结构化加权稀疏低秩恢复算法在人脸识别中的应用[J]. 智能系统学报, 2019, 14(3): 455-463.
WU Xiaoyi, WU Xiaojun. A low rank recovery algorithm for face recognition with structured and weighted sparse constraint[J]. CAAI transactions on intelligent systems, 2019, 14(3): 455-463.
[11] KOLDA T G, BADER B W. Tensor decompositions and applications[J]. SIAM review, 2009, 51(3): 455-500.
[12] KILMER M E, BRAMAN K, HAO Ning, et al. Third-order tensors as operators on matrices: a theoretical and computational framework with applications in imaging[J]. SIAM journal on matrix analysis and applications, 2013, 34(1): 148-172.
[13] LIU Ji, MUSIALSKI P, WONKA P, et al. Tensor completion for estimating missing values in visual data[J]. IEEE transactions on pattern analysis and machine intelligence, 2013, 35(1): 208-220.
[14] HUANG Bo, MU Cun, GOLDFARB Donald, et al. Provable models for robust low-rank tensor completion[J]. Pacific journal of optimization, 2015, 11(2): 339-64.
[15] LU Canyi, FENG Jiashi, CHEN Yudong, et al. Tensor robust principal component analysis with a new tensor nuclear norm[J]. IEEE transactions on pattern analysis and machine intelligence, 2020, 42(4): 925-938.
[16] KILMER M E, MARTIN C D. Factorization strategies for third-order tensors[J]. Linear algebra and its applications, 2011, 435(3): 641-658.
[17] ZHANG Zemin, ELY G, AERON S, et al. Novel methods for multilinear data completion and de-noising based on tensor-SVD[C]//2014 IEEE Conference on Computer Vision and Pattern Recognition. Columbus: IEEE, 2014: 3842-3849.
[18] LU Canyi, FENG Jiashi, CHEN Yudong, et al. Tensor robust principal component analysis: exact recovery of corrupted low-rank tensors via convex optimization[C]//2016 IEEE Conference on Computer Vision and Pattern Recognition. Las Vegas: IEEE, 2016: 5249-5257.
[19] BOYD S. Distributed optimization and statistical learning via the alternating direction method of multipliers[J]. Foundations and trends? in machine learning, 2010, 3(1): 1-122.
[20] CANDèS E J, WAKIN M B, BOYD S P. Enhancing sparsity by reweighted ?1 minimization[J]. Journal of fourier analysis and applications, 2008, 14(5): 877-905.
[21] GENG Xiaoyu, GUO Qiang, HUI Shuaixiong, et al. Tensor robust PCA with nonconvex and nonlocal regularization[J]. Computer vision and image understanding, 2024, 243: 104007.
[22] ZHANG Feng, WANG Hailin, QIN Wenjin, et al. Generalized nonconvex regularization for tensor RPCA and its applications in visual inpainting[J]. Applied intelligence, 2023, 53(20): 23124-23146.
[23] YANG Ming, LUO Qilun, LI Wen, et al. Nonconvex 3D array image data recovery and pattern recognition under tensor framework[J]. Pattern recognition, 2022, 122: 108311.
[24] WANG Hailin, ZHANG Feng, WANG Jianjun, et al. Generalized nonconvex approach for low-tubal-rank tensor recovery[J]. IEEE transactions on neural networks and learning systems, 2022, 33(8): 3305-3319.
[25] 苏雅茹, 刘耿耿, 刘文犀, 等. 基于lP范数的非凸低秩张量最小化[J]. 模式识别与人工智能, 2019, 32(6): 494-503.
SU Yaru, LIU Genggeng, LIU Wenxi, et al. Nonconvex low-rank tensor minimization based on lP norm[J]. Pattern recognition and artificial intelligence, 2019, 32(6): 494-503.
[26] GENG Xiaoyu, GUO Qiang, ZHANG Caiming. Color image denoising via tensor robust PCA with nonconvex and nonlocal regularization[C]//ACM multimedia Asia. Gold Coast: ACM, 2021: 1-5.
[27] WEN Fei, YING Rendong, LIU Peilin, et al. Robust PCA using generalized nonconvex regularization[J]. IEEE transactions on circuits and systems for video technology, 2020, 30(6): 1497-1510.
[28] GAO Quanxue, ZHANG Pu, XIA Wei, et al. Enhanced tensor RPCA and its application[J]. IEEE transactions on pattern analysis and machine intelligence, 2021, 43(6): 2133-2140.
[29] YANG Jinghua, ZHAO Xile, MA Tianhui, et al. Tensor train rank minimization with hybrid smoothness regularization for visual data recovery[J]. Applied mathematical modelling, 2020, 81: 711-726.
[30] 杨枥皓. 基于截断核范数张量鲁棒主成分分析[J]. 人工智能与机器人研究, 2020, 9: 64.
YANG Lihao. Tensor Robust Principal Component Analysis Based on Truncated Nuclear Norm[J]. Artificial intelligence and robotics research, 2020, 9: 64.
[31] 陈利霞, 班颖, 王学文. 基于张量核范数与3D全变分的背景减除[J]. 计算机应用, 2020, 40(9): 2737-2742.
CHEN Lixia, BAN Ying, WANG Xuewen. Background subtraction based on tensor nuclear norm and 3D total variation[J]. Journal of computer applications, 2020, 40(9): 2737-2742.
[32] TIBSHIRANI R. Regression shrinkage and selection via the lasso: a retrospective[J]. Journal of the royal statistical society series B: statistical methodology, 2011, 73(3): 273-282.
[33] ZUO Wangmeng, MENG Deyu, ZHANG Lei, et al. A generalized iterated shrinkage algorithm for non-convex sparse coding[C]//2013 IEEE International Conference on Computer Vision. Sydney: IEEE, 2013: 217-224.
[34] MIRSKY L. A trace inequality of john von Neumann[J]. Monatshefte für mathematik, 1975, 79(4): 303-306.
[35] 李坤来, 王雲龙, 秦琴, 等. MATLAB中多种图像去噪算法的比较分析[J]. 信息技术与信息化, 2023(8): 62-67.
LI Kunlai, WANG Yunlong, QIN Qin, et al. Comparative analysis of various image denoising algorithms in MATLAB[J]. Information technology and informatization, 2023(8): 62-67.
[36] 史凯特, 孙浩东, 董秀芬, 等. 基于改进加权核范数最小化的图像去噪算法研究[J]. 电光与控制, 2024: 48-52.
SHI Kaite, SUN Haodong, DONG Xiufen, et al. Research on image denoising algorithm based on improved weighted kernel norm minimization[J]. China industrial economics, 2024: 48-52.
[37] MORDVINTSEV Alexander, OLAH Christopher, TYKA Mike. Inceptionism: going deeper into neural networks[J]. Google research blog, 2015, 20(14): 5-15.
[38] MAHENDRAN A, VEDALDI A. Visualizing deep convolutional neural networks using natural pre-images[J]. International journal of computer vision, 2016, 120(3): 233-255.
[39] XIE Qi, ZHAO Qian, MENG Deyu, et al. Kronecker-basis-representation based tensor sparsity and its applications to tensor recovery[J]. IEEE transactions on pattern analysis and machine intelligence, 2018, 40(8): 1888-1902.
[40] LIU Youfa, DU Bo, CHEN Yongyong, et al. Convex–concave tensor robust principal component analysis[J]. International journal of computer vision, 2024, 132(5): 1721-1747.
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