标题： 具有自引导数据增强的离群值感知张量鲁棒主成分分析 显示英文标题

标题： Outlier-aware Tensor Robust Principal Component Analysis with Self-guided Data Augmentation

摘要： 张量鲁棒主成分分析（TRPCA）是一种基本技术，用于将多维数据分解为低秩张量和异常值张量，但现有依赖稀疏异常假设的方法往往在存在结构化破坏时失效。 本文提出了一种自引导的数据增强方法，采用自适应加权来抑制异常值的影响，将原始的TRPCA问题重新表述为标准的张量主成分分析（TPCA）问题。 所提出的模型包括一种基于优化的加权方案，在张量增强过程中动态识别并降低异常值的贡献。 我们开发了一种高效的近端块坐标下降算法，并通过闭式更新解决由此产生的优化问题，确保计算效率。 通过结合块坐标下降与重大化最小化原则的框架，保证了理论上的收敛性。 在合成数据集和真实世界数据集上的数值实验，包括人脸恢复、背景减除和高光谱去噪，表明我们的方法能够有效处理各种破坏模式。 结果显示，与最先进的方法相比，我们的方法在准确性和计算效率方面均有提升。 显示英文摘要

摘要： Tensor Robust Principal Component Analysis (TRPCA) is a fundamental technique for decomposing multi-dimensional data into a low-rank tensor and an outlier tensor, yet existing methods relying on sparse outlier assumptions often fail under structured corruptions. In this paper, we propose a self-guided data augmentation approach that employs adaptive weighting to suppress outlier influence, reformulating the original TRPCA problem into a standard Tensor Principal Component Analysis (TPCA) problem. The proposed model involves an optimization-driven weighting scheme that dynamically identifies and downweights outlier contributions during tensor augmentation. We develop an efficient proximal block coordinate descent algorithm with closed-form updates to solve the resulting optimization problem, ensuring computational efficiency. Theoretical convergence is guaranteed through a framework combining block coordinate descent with majorization-minimization principles. Numerical experiments on synthetic and real-world datasets, including face recovery, background subtraction, and hyperspectral denoising, demonstrate that our method effectively handles various corruption patterns. The results show the improvements in both accuracy and computational efficiency compared to state-of-the-art methods.