Electromagnetic Source Imaging via Bayesian Modeling With Smoothness in Spatial and Temporal Domains

Accurate reconstruction of cortical activation from electroencephalography and magnetoencephalography (E/MEG) is a long-standing challenge because of the inherently ill-posed inverse problem. In this paper, a novel algorithm under the empirical Bayesian framework, source imaging with smoothness in spatial and temporal domains (SI-SST), is proposed to address this issue. In SI-SST, current sources are decomposed into the product of spatial smoothing kernel, sparseness encoding coefficients, and temporal basis functions (TBFs). Further smoothness is integrated in the temporal domain with the employment of an underlying autoregressive model. Because sparseness encoding coefficients are constructed depending on overlapped clusters over cortex in this model, we derived a novel update rule based on fixed-point criterion instead of the convexity based approach which becomes invalid in this scenario. Entire variables and hyper parameters are updated alternatively in the variational inference procedure. SI-SST was assessed by multiple metrics with both simulated and experimental datasets. In practice, SI-SST had the superior reconstruction performance in both spatial extents and temporal profiles compared to the benchmarks.