Bayesian Dictionary Learning on Robust Tubal Transformed Tensor Factorization

Area of Science:

• Multidimensional data analysis
• Tensor decomposition
• Machine learning

Background:

• Tensor singular value decomposition (t-SVD) shows promise for multidimensional data recovery.
• Fixed transformations in t-SVD limit adaptability to diverse datasets.
• Exploiting low-rank and sparse properties requires flexible methods.

Purpose of the Study:

• To develop a data-driven dictionary learning (DL) model for tensor robust principal component analysis (TRPCA).
• To enhance the identification of underlying low-tubal-rank structures in tensors.
• To improve the flexibility and effectiveness of multidimensional data recovery.

Main Methods:

• Constructing a data-driven dictionary from observed noisy data along tensor tubes.
• Employing a Bayesian DL model with tensor tubal transformed factorization.
• Utilizing a variational Bayesian DL algorithm with pagewise tensor operators.

Main Results:

• The proposed method effectively identifies low-tubal-rank structures using a data-adaptive dictionary.
• The approach demonstrates superior performance in multidimensional data recovery compared to fixed transformations.
• Experiments show effectiveness and efficiency in real-world applications like image denoising and separation.

Conclusions:

• The developed Bayesian DL model offers a flexible and effective solution for TRPCA.
• Data-adaptive dictionaries significantly improve the exploitation of tensor properties.
• The approach shows strong potential for various real-world multidimensional data processing tasks.