Numerical resolution of the inverse source problem for EEG using the quasi-reversibility method

Marion Darbas (1) , Juliette Leblond (2) , Jean-Paul Marmorat (3) , Pierre-Henri Tournier (4, 5)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 FACTAS - Analyse fonctionnelle pour la conception et l'analyse de systèmes
3 CMA - Centre de Mathématiques Appliquées
4 ALPINES - Algorithms and parallel tools for integrated numerical simulations
5 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

We propose a numerical method for solving a family of source estimation inverse problems from Cauchy data for Poisson (conductivity) PDE in non-homogeneous domains. The targeted application is the electroencephalography (EEG) dipolar source localization problem in brain imaging, for which it allows to take into account the specific heterogeneity of the skull in the data transmission step (cortical mapping) from the scalp to the cortex.

Keywords: Inverse problems elliptic PDE quasi-reversibility best constrained approximation brain imaging (EEG); Inverse problems; elliptic PDE; quasi-reversibility; best constrained approximation; brain imaging (EEG)

Domains: Mathematics [math]

Marion Darbas, Juliette Leblond, Jean-Paul Marmorat, Pierre-Henri Tournier. Numerical resolution of the inverse source problem for EEG using the quasi-reversibility method. 2022. ⟨hal-03880526v1⟩