Section: New Results

Forward and Inverse Problems in MEEG

Source localization using rational approximation on plane sections

Participants : Maureen Clerc [Athena Project-Team, Inria, Sophia Antipolis, Méditerranée, France] , Théodore Papadopoulo [Athena Project-Team, Inria, Sophia Antipolis, Méditerranée, France] , Juliette Leblond [Apics Project-Team, Inria, Sophia Antipolis, Méditerranée, France] , Jean-Paul Marmorat [CMA, Ecole des Mines Paristech, Sophia Antipolis, France] .

In functional neuroimaging, a crucial problem is to localize active sources within the brain non-invasively, from knowledge of electromagnetic measurements outside the head. Identification of point sources from boundary measurements is an ill-posed inverse problem. In the case of electroencephalography (EEG), measurements are only available at electrode positions, the number of sources is not known in advance and the medium within the head is inhomogeneous. We have presented  [49] a new method for EEG source localization, based on rational approximation techniques in the complex plane. The method is used in the context of a nested sphere head model, in combination with a cortical mapping procedure. Results on simulated data prove the applicability of the method in the context of realistic measurement configurations. In the continuation of this work, we are in discussion with an industrial partner (BESA, Munich) for a scientific partnership.

Dictionary learning for multitrial datasets

Participants : Maureen Clerc, Sebastian Hitziger, Théodore Papadopoulo.

Following the path opened with the Consensus matching Pursuit method (CMP) [46] , we continue our endeavour to avoid signal averaging using directly the raw signal with the assumption that events of interest are those that repeat in each trial [36] . Towards such a goal, and to improve the simple dictionary used in CMP, we have adapted dictionary learning methods to multitrial bio-electric signals, by explicitly implementing jitter invariance [30] . This allows for a much more detailed data-driven description of events. For example, using local field potential signals of chemically induced spikes (in a rat model), we have been able to distinguish several spike shapes which show some coherence in time. The method has been recently extended to detect spike events in continuous signals (i.e. not organized in epochs). While it requires a good signal to noise ratio, the method is very general and has also been used for various other signal types (see section  6.5 ).