Variational Bayesian Inference for Tensor Robust Principal Component Analysis

TL;DR

This paper introduces a Bayesian approach to Tensor Robust Principal Component Analysis that automatically balances low-rank and sparse noise components, improving accuracy in noisy data recovery.

Contribution

It proposes a novel Bayesian framework with adaptive priors for TRPCA, enhancing low-rank tensor recovery and noise separation over existing methods.

Findings

Outperforms state-of-the-art TRPCA methods on synthetic datasets.

Effectively balances low-rank and sparse components in real-world data.

Extensible to weighted tensor nuclear norm models.

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.