Apprentissage automatique pour la résolution de problème inverse pour l’étude de l’activité électrophysiologique du cerveau

EEG source imaging (ESI) aims to estimate the activity of neuronal sources in the brain, based on the electroencephalography (EEG) signal. This is an ill-posed inverse problem, requiring the addition of a priori information about the solution in order to solve it. In the context of ESI, many different a priori have been proposed but choosing one remains difficult for brain activity, which is a particularly complex signal. This thesis explores the use of supervised learning methods for ESI. Simulated data are used to train neural networks in a supervised manner. Two types of approaches are explored, as well as their ability to generalize out of the training data distribution. Direct inversion approaches give very good results, in an idealized case. To obtaina more realistic method, a model-based approach that integrates information from the direct model into the training framework is studied. The approach chosen allows to learn the prior term in a variational cost, together with the solver for minimizing this cost. In this context, the use of graph neural networks offers greater flexibility with regard to the head model.