Electromagnetic source imaging (ESI) and independent component analysis (ICA) are two popular and apparently dissimilar frameworks for M/EEG analysis. This letter shows that the two frameworks can be linked by choosing biologically inspired source sparsity priors. We demonstrate that ESI carried out by the sparse Bayesian learning (SBL) algorithm yields source configurations composed of a few active regions that are also maximally independent from one another. In addition, we extend the standard SBL approach to source imaging in two important directions. First, we augment the generative model of M/EEG to include artifactual sources. Second, we modify SBL to allow for efficient model inversion with sequential data. We refer to this new algorithm as recursive SBL (RSBL), a source estimation filter with potential for online and offline imaging applications. We use simulated data to verify that RSBL can accurately estimate and demix cortical and artifactual sources under different noise conditions. Finally, we show that on real error-related EEG data, RSBL can yield single-trial source estimates in agreement with the experimental literature. Overall, by demonstrating that ESI can produce maximally independent sources while simultaneously localizing them in cortical space, we bridge the gap between the ESI and ICA frameworks for M/EEG analysis.