Variational Bayesian Inference for Tensor Robust Principal Component Analysis

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Abstract
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.
Funding Information
  • Guangdong Basic and applied Research Foundation (2024A1515012347)
  • National Natural Science Foundation of China (12361089)
  • National Natural Science Foundation of China (12201286)
  • HKRGC (LU13300125)
  • HKRGC (LU11309922)
  • ITF (MHP/054/22)
  • ITF (LU BGR 105824)

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