Inverse EEG source problems and approximation
Mohamed Fahmi Ben Hassen, Maureen Clerc, Juliette Leblond, Stéphane Rigat, Meriem Zghal · 2008
regularization techniques; reconstruction techniques, robust optimization; applications: non-destructive evaluation, inverse problems in biomedical engineering. We consider the inverse EEG (ElectroEncephaloGraphy) problem that consists in recovering, from measurements on electrodes of the electric potential on the scalp, a distribution of pointwise dipolar current sources located in the brain and modeling e.g. the presence of epileptic foci. The head Ω = ∪ 2 i=0 Ωi ⊂ R 3 is modeled as a set of nested regions Ωi ⊂ R 3, i = 0, 1, 2 (brain, skull, scalp), separated by either spherical or ellipsoidal interfaces Si (with S2 = ∂Ω) and with piecewise constant conductivity σ, σ |Ω i = σi> 0. Considering a macroscopic physical model of brain activity and using a quasi-static approximation of the Maxwell equations, see [1], the spatial behaviour of the electric potential u in Ω is related to the distribution of m dipolar sources located at Ck ∈ Ω0 with moments pk ∈ R3 by Poisson equation: (P) { ∑m div (σ∇u) =