  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.
