[1]潘昱妍,张德,李壮举.融合低秩预分离与随机抖动机制的非凸型TRPCA算法[J].智能系统学报,2025,20(4):822-837.[doi:10.11992/tis.202406003]
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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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]
融合低秩预分离与随机抖动机制的非凸型TRPCA算法
《智能系统学报》[ISSN 1673-4785/CN 23-1538/TP] 卷:
20
期数:
2025年第4期
页码:
822-837
栏目:
学术论文—机器学习
出版日期:
2025-08-05
- Title:
- Nonconvex TRPCA algorithm combined with low-rank pre-separation and random jitter mechanism
- Keywords:
- principal component analysis; tensor; image denoising; image processing; machine learning; computer application; signal processing; singular value decomposition
- 分类号:
- TP391
- 文献标志码:
- 2025-2-24
- 摘要:
- 为了解决张量鲁棒主成分分析(tensor robust principal component analysis, TRPCA)还原低秩结构时同等收缩奇异值造成的信息提取偏差问题，本文考虑区别对待奇异值，使用非凸加权张量Schatten-p范数(0<p<1)分析张量数据，可减少对奇异值的惩罚。为解决数据受损严重难以恢复的问题，提出低秩预分离的方法实现近似低秩部分和近似稀疏部分的预先分离；为增强高阶张量之间相关性同时降低数据对特定噪声的敏感性，提出随机抖动正则器的机制对预分离后成分分别选取随机区域优化，利用噪声信息的随机性来正则化算法得以约束模型的复杂度；最后使用不同类型的图像数据集，包括彩色图像、核磁共振图像、高光谱及多光谱图像和灰度视频，进行高维数据恢复实验。结果表明该方法在图像恢复性能上明显优于其他TRPCA方法，并且在数据受损严重时同样具有优势，有效提取主成分信息的同时减小数据对特定噪声的依赖，具有较强的鲁棒性和适应性，可为TRPCA方法在图像恢复领域中提供参考。
- 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.
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备注/Memo
收稿日期:2024-6-3。
基金项目:国家自然科学基金项目（62271035）；北京市自然科学基金项目（4232021）.
作者简介:潘昱妍，硕士研究生，主要研究方向为机器学习和图像处理。E-mail：13439684118@163.com。;张德，副教授，博士，主要研究方向为计算机视觉和模式识别。E-mail：zhangde2000@163.com。;李壮举，副教授，博士，主要研究方向为机器人智能控制和建筑节能控制技术。E-mail：lizhuangju@bucea.edu.cn。
通讯作者:张德. E-mail：zhangde2000@163.com
更新日期/Last Update:
1900-01-01