A hierarchical Krylov-Bayes iterative inverse solver for MEG with anatomical prior

In the present study, we revisit the MEG inverse problem, regularization and depth weighting from a Bayesian hierarchical point of view: the primary unknown is the discretized current density and each dipole has a preferred direction extracted from the MRI of the subject and encoded in the prior distribution. The variance of each dipole is described by its hyperprior density: this hypermodel is used to build the Iterative Alternating Sequential (IAS) algorithm with the novel feature that the parameters are determined using an empirical Bayes approach. We test the performance of the IAS algorithm against synthetic but realistic data. We simulate the neural activity generated by cortical patches located in several cerebral regions including deep regions as Insula, posterior Cingulate, Cerebellum and Hippocampus. Then, we reconstruct the activity by the IAS method with and without the physiological prior. The tests show that the physiological prior significantly improves the localization of the activity also in the case when the neural sources are located in deep regions. We compare the performance of the IAS method against the results obtained using two of the most popolar inversion methods: wMNE and dSPM. A measure based on Bayesian factors is used to quantify the reliability of the reconstructions. Finally, the three inversion methods are applied to a set of auditory real data. The Bayesian hierarchical model provides a very natural interpretation for sensitivity weighting, and the parameters in the hyperprior provide a tool for controlling the quality of the solution in terms of focality, thus leading to a flexible algorithm that can handle both sparse and distributed sources. References 1. Calvetti D, Pitolli F, Somersalo E and Vantaggi B(2015) ArXiv:1503.06844 2. Calvetti D, Pascarella A, Pitolli F, Somersalo E and Vantaggi B(2015) Inverse Problems 31(12) 3. Lin FH et al.(2006) Neuroimage 31 160-171 4. Tadel et al.(2011) Computational intelligence and neuroscience, 2011:8