Sparse EEG Source Localization Using Bernoulli Laplacian Priors

Facundo Costa*, Hadj Batatia, Lotfi Chaari, Jean-Yves Tourneret

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


Source localization in electroencephalography has received an increasing amount of interest in the last decade. Solving the underlying ill-posed inverse problem usually requires choosing an appropriate regularization. The usual ℓ2 norm has been considered and provides solutions with low computational complexity. However, in several situations, realistic brain activity is believed to be focused in a few focal areas. In these cases, the ℓ2 norm is known to overestimate the activated spatial areas. One solution to this problem is to promote sparse solutions for instance based on the ℓ1 norm that are easy to handle with optimization techniques. In this paper, we consider the use of an ℓ0 + ℓ1 norm to enforce sparse source activity (by ensuring the solution has few nonzero elements) while regularizing the nonzero amplitudes of the solution. More precisely, the ℓ0 pseudonorm handles the position of the nonzero elements while the ℓ1 norm constrains the values of their amplitudes. We use a Bernoulli-Laplace prior to introduce this combined ℓ0 + ℓ1 norm in a Bayesian framework. The proposed Bayesian model is shown to favor sparsity while jointly estimating the model hyperparameters using a Markov chain Monte Carlo sampling technique. We apply the model to both simulated and real EEG data, showing that the proposed method provides better results than the ℓ2 and ℓ1 norms regularizations in the presence of pointwise sources. A comparison with a recent method based on multiple sparse priors is also conducted.

Original languageEnglish
Pages (from-to)2888-2898
Number of pages11
JournalIEEE Transactions on Biomedical Engineering
Issue number12
Publication statusPublished - Dec 2015


  • Electroencephalography (EEG)
  • inverse problem
  • Markov chain monte carlo (MCMC)
  • source localization
  • sparse Bayesian restoration
  • ℓ + ℓ norm regularization

ASJC Scopus subject areas

  • Biomedical Engineering


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