Joint Learning of Full-Structure Noise in Hierarchical Bayesian Regression Models

Area of Science:

• Neuroscience and Biomedical Engineering
• Computational Statistics
• Signal Processing

Background:

• Reconstructing brain activity from electroencephalography (EEG) is a critical inverse problem.
• Accurate source estimation depends on understanding noise characteristics, including its correlation structure.
• Existing methods often oversimplify noise models, limiting reconstruction accuracy.

Purpose of the Study:

• To develop advanced hierarchical Bayesian models for joint estimation of brain activity sources and noise covariance.
• To extend sparse Bayesian learning (SBL) to handle full-structured noise covariance.
• To improve the accuracy of brain activity reconstruction in realistic scenarios.

Main Methods:

• Developed hierarchical Bayesian (Type-II Maximum Likelihood) models incorporating latent variables for source and noise.
• Extended sparse Bayesian learning (SBL) to account for full Gaussian noise covariance.
• Utilized majorization-maximization and Riemannian geometry for efficient noise covariance updates.

Main Results:

• The proposed algorithm demonstrates guaranteed and fast convergence.
• Validated performance through simulations and real magnetoencephalography (MEG) data.
• Significantly outperformed state-of-the-art techniques when noise is non-diagonal and full-structured.

Conclusions:

• The novel Bayesian framework effectively models and estimates full-structured noise in EEG/MEG data.
• This approach substantially enhances brain activity reconstruction accuracy.
• The method has broad applicability in various inverse problems beyond neuroimaging.