新方法通过自引导增强抑制异常值影响，提升多维数据去噪效果。
Outlier-aware Tensor Robust Principal Component Analysis with Self-guided Data Augmentation
- 用自适应加权动态识别并降低异常值影响，将TRPCA转为标准TPCA问题。
- 在人脸恢复、背景分割等任务中，准确率和效率均优于现有方法。
- 适合处理结构化异常的多维数据，如图像、高光谱数据去噪场景。
张量鲁棒主成分分析（TRPCA）是分解多维数据为低秩张量与异常张量的基础方法，但现有依赖稀疏异常假设的方法在面对结构化污染时表现不佳。本文提出一种自引导数据增强方法，通过自适应加权抑制异常值影响，将原TRPCA问题重构为标准张量主成分分析（TPCA）问题。模型采用优化驱动的加权机制，在张量增强过程中动态识别并下调异常贡献。我们设计了一种具有闭式更新的近端块坐标下降算法，有效求解优化问题，确保计算高效；理论收敛性基于块坐标下降与极大化-极小化原理相结合的框架。在合成及真实世界数据集上的实验，涵盖人脸恢复、背景减除和高光谱去噪，验证了该方法对多种污染模式的有效性。结果表明，相比当前最优方法，本方法在精度和计算效率上均有提升。
原文摘要 · Abstract (English)
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.
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