Variational Bayesian Inference for Tensor Robust Principal Component Analysis
This work addresses challenges in TRPCA for machine learning and computer vision applications, offering an incremental improvement by automating parameter tuning in mixed-noise scenarios.
The paper tackled the problem of Tensor Robust Principal Component Analysis (TRPCA) by introducing a Bayesian framework that integrates low-rank tensor nuclear norm and sparsity-inducing priors to automatically balance low-rank and sparse components, achieving superior performance on synthetic and real-world datasets compared to state-of-the-art methods.
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 characterizing 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 proposed 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.