We examine Hierachical Bayesian approaches to solve the under-determined and severely ill-posed inverse problem of EEG/MEG source reconstruction. For Laplacian scale mixture models, we show how a combination of Markov Chain Monte-Carlo methods and convex optimization techniques can be used to explore the different modes of the posterior distribution and thereby quantify the inherent uncertainty and ambiguity of such ill-posed inference procedures. Joint work with Yousra Bekhti, Joseph Salmon and Alexandre Gramfort.

This presentation is part of Minisymposium “MS19 - Brain imaging: from neurosignals to functional brain mapping”
organized by: Erkki Somersalo (Case Western Reserve University) , Francesca Pitolli (Dept. of Basic and Applied Sciences for Engineering, University of Rome “La Sapienza”) .

Authors:

Felix Lucka (CWI & UCL)

Keywords:

bayesian methods, image deblurring, image reconstruction, inverse problems, statistical inverse estimation methods