Numerical resolution of the inverse source problem for EEG using the quasi-reversibility method

The paper concerns the numerical resolution of the inverse source problem for electroencephalography. We propose an approach which is able to take into account some heterogeneity properties (namely a varying electrical conductivity) of the head tissues, in particular of the skull layer. It combines two consecutive steps: (i) a data completion procedure from the scalp to the cortex using the quasi-reversibility method, (ii) a source estimation method from these cortical transmitted data within the brain (modeled as sphere), developed in the software tool FindSources3D. Numerical simulations in the case of the multi-layered spherical head model illustrate both the promising and limiting features of the approach.

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