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.

翻译：张量鲁棒主成分分析（TRPCA）在机器学习和计算机视觉领域具有重要地位，其目标在于恢复潜在的低秩结构并表征噪声的稀疏结构。现有方法通常难以准确捕捉张量的低秩特性，且在低秩分量与稀疏分量间的权衡方面存在困难，尤其在混合噪声场景下更为突出。为应对这些挑战，本文提出一种TRPCA的贝叶斯框架，该框架融合了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，我们的方法能够自动确定最优张量核范数，并实现核范数与稀疏分量间的平衡。此外，本方法可高效扩展至加权张量核范数模型。在合成数据集与真实数据集上的实验表明，相较于现有先进方法，本方法具有显著的有效性与优越性。