用贝叶斯方法自动平衡张量低秩与稀疏性，提升去噪性能。
Variational Bayesian Inference for Tensor Robust Principal Component Analysis
- 引入低秩张量核范数和稀疏诱导先验的贝叶斯框架
- 自动确定最优核范数，有效分离低秩与稀疏噪声
- 适用于混合噪声场景，适合数据恢复与计算机视觉任务
张量鲁棒主成分分析（TRPCA）在机器学习和计算机视觉中具有关键作用，旨在恢复底层低秩结构并表征噪声的稀疏特性。现有方法在准确捕捉张量低秩属性及平衡低秩与稀疏分量方面常遇困难，尤其在混合噪声环境下。为此，本文提出一种基于贝叶斯框架的TRPCA方法，结合低秩张量核范数先验与广义稀疏诱导先验。通过将先验嵌入贝叶斯框架，本方法可自动确定最优张量核范数，实现核范数与稀疏分量间的良好平衡。此外，该方法可高效扩展至加权张量核范数模型。在合成与真实数据集上的实验表明，其性能优于当前主流方法。
原文摘要 · Abstract (English)
Tensor Robust Principal Component Analysis (TRPCA) holds a crucial position in machine learning and computer vision. It aims to recover underlying low-rank structures and to characterize the sparse structures of noise. Current approaches often encounter difficulties in accurately capturing the low-rank properties of tensors and balancing the trade-off between low-rank and sparse components, especially in a mixed-noise scenario. To address these challenges, we introduce a Bayesian framework for TRPCA, which integrates a low-rank tensor nuclear norm prior and a generalized sparsity-inducing prior. By embedding the priors within the Bayesian framework, our method can automatically determine the optimal tensor nuclear norm and achieve a balance between the nuclear norm and sparse components. Furthermore, our method can be efficiently extended to the weighted tensor nuclear norm model. Experiments conducted on synthetic and real-world datasets demonstrate the effectiveness and superiority of our method compared to state-of-the-art approaches.
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