EEG source localization based on a structured sparsity prior and a partially collapsed Gibbs sampler

Facundo Hernan Costa (1, 2) , Hadj Batatia (1, 2) , Thomas Oberlin (3, 2) , Jean-Yves Tourneret (4, 2)

1 IRIT-TCI - Traitement et Compréhension d’Images
2 Toulouse INP - Institut National Polytechnique (Toulouse)
3 IRIT-SC - Signal et Communications
4 IRIT-MINDS - CoMputational imagINg anD viSion

In this paper, we propose a hierarchical Bayesian model approximating the ℓ20 mixed-norm regularization by a multivariate Bernoulli Laplace prior to solve the EEG inverse problem by promoting spatial structured sparsity. The posterior distribution of this model is too complex to derive closed-form expressions of the standard Bayesian estimators. An MCMC method is proposed to sample this posterior and estimate the model parameters from the generated samples. The algorithm is based on a partially collapsed Gibbs sampler and a dual dipole random shift proposal for the non-zero positions. The brain activity and all other model parameters are jointly estimated in a completely unsupervised framework. The results obtained on synthetic data with controlled ground truth show the good performance of the proposed method when compared to the ℓ21 approach in different scenarios, and its capacity to estimate point-like source activity.

Mots clés: ℓ20-norm regularization; Hierarchical Bayesian model; Structured-sparsity; Inverse problem; Source localization; MCMC; EEG

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]; Intelligence artificielle [cs.AI]; Vision par ordinateur et reconnaissance de formes [cs.CV]; Traitement des images [eess.IV]; Traitement du signal et de l'image [eess.SP]

Facundo Hernan Costa, Hadj Batatia, Thomas Oberlin, Jean-Yves Tourneret. EEG source localization based on a structured sparsity prior and a partially collapsed Gibbs sampler. 6th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2015), Dec 2015, Cancun, Mexico. pp.261-264. ⟨hal-01491206⟩