"Spectral graph wavelets penalization for M/EEG distributed inverse problem"MOKHTARI, SamyMagneto and Electroencephalography (M/EEG) are brain imaging modalities used to measure the electrical activity of the brain. M/EEG source reconstruction problems, which consist in explaining a few hundreds measurement points with several thousands of current dipoles within the cortex, are strongly ill-posed. As a consequence, additional constraints are required in order to promote specific solutions in the resolution of the inverse problem. These constraints can be formulated in a Bayesian framework, using prior informations and assumptions on the distribution of the noise and sources. In order to mimick the fact that only a few brain regions are generally active during a task, these additional constraints may also be formulated as penalization terms specifically designed to promote sparsity, and thus improve the spatial localization of the reconstructed sources. In a will to enrich the already existing approaches based on l1-norm or total variation, a penalization based on spectral graph wavelets coefficients (cf. the work of D. K. Hammond, P. Vandergheynst and R. Gribonval) is here proposed. The relevance of this wavelet-based penalization (in terms of spatial localization and accuracy with respect to the order of magnitude of the targeted data) will be detailed with real and simulated M/EEG data. |
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