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How to map and track brain activations with M/EEG using sparse priors and graph cuts

Magneto and electroencephalography (M/EEG) can measure every millisecond the electromagnetic fields produced by the brain. From these measurements, the challenge is to localize in space, but also in time, the active brain regions that have generated the measured signal. This source localization problem is referred to as the M/EEG inverse problem. After a short introduction to the biological basis and the physics principles enabling the acquisition of M/EEG data, we will detail the mathematical and computational aspects of the M/EEG inverse problem. When considering distributed source models, the problem addressed is strongly ill-posed. In this framework, related problems are the blind source separation problems in audio processing and the deconvolution problems in image processing. Since the problem is ill-posed a priori knowledge needs to be used. In this presentation, we will focus on priors leading to convex optimization problems for which we will present general optimization strategies based on proximity operators (Forward-Backward, Nesterov iterative schemes). These priors are based on L1, L1/L2 mixed norms and the total variation computed over a triangulated mesh. We will show how this framework allowed us to provide a solution to the problem of retinotopic mapping with MEG data. Then, we will detail a graph-cut based tracking algorithm that we used to follow cortical activations over time in the human primary visual cortex.

Keywords : MEG, EEG, Brain Functional Imaging, Inverse Problems, Convex optimization, Proximal operators, Graph-Cuts Optimization


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