Bayesian Structured Sparsity Priors for EEG Source Localization Technical Report

TL;DR

This paper presents a hierarchical Bayesian model with structured sparsity priors for EEG source localization, improving focal brain activity detection through a novel sampling approach and hyperparameter estimation.

Contribution

It introduces a new Bayesian hierarchical model with structured sparsity priors and a partially collapsed Gibbs sampler for EEG source localization.

Findings

Outperforms weighted ℓ₁₋₂ regularization in synthetic data.

Shows advantages over multiple sparse prior methods on real data.

Accelerates convergence with novel Metropolis-Hastings moves.

Abstract

This report introduces a new hierarchical Bayesian model for the EEG source localization problem. This model promotes structured sparsity to search for focal brain activity. This sparsity is obtained via a multivariate Bernoulli Laplacian prior assigned to the brain activity approximating an $\ell_{20}$ pseudo norm regularization in a Bayesian framework. A partially collapsed Gibbs sampler is used to draw samples asymptotically distributed according to the posterior associated with the proposed Bayesian model. The generated samples are used to estimate the brain activity and the model hyperparameters jointly in an unsupervised framework. Two different kinds of Metropolis-Hastings moves are introduced to accelerate the convergence of the Gibbs sampler. The first move is based on multiple dipole shifts within each MCMC chain whereas the second one exploits proposals associated with different MCMC chains. We use both synthetic and real data to compare the performance of the proposed method with the weighted $\ell_{21}$ mixed norm regularization and a method based on a multiple sparse prior, showing that our algorithm presents advantages in several scenarios.