Identifiability Properties for Inverse Problems in EEG Data Processing and Medical Engineering with Observability and Optimization Issues

Juliette Leblond (1)

1 APICS - Analysis and Problems of Inverse type in Control and Signal processing

We consider inverse problems of source identification in electroen-cephalography, modelled by elliptic partial differential equations. Being given boundary data that consist in values of the current flux and of the electric poten-tial on the scalp, the aim is to reconstruct unknown current sources supported within the brain. For spherical layered models of the head, and after a pre-liminary data transmission step, such inverse source problems are tackled using best rational approximation techniques on planar sections. Both theoretical and constructive aspects are described, while numerical illustrations are provided.

Mots clés: EEG (electroencephalography); observability; medical imaging; elliptic partial differential equa-tion; Inverse boundary value problems; optimiza-tion

Domaines: Equations aux dérivées partielles [math.AP]

Juliette Leblond. Identifiability Properties for Inverse Problems in EEG Data Processing and Medical Engineering with Observability and Optimization Issues. Acta Applicandae Mathematicae, 2014, 135 (1), pp. 175-190. ⟨10.1007/s10440-014-9951-7⟩. ⟨hal-00875006v2⟩