Abstract This article presents a new spatio-temporal method for M/EEG source reconstruction based on the assumption that only a small number of events, localized in space and/or time, are responsible for the measured signal. Each space–time event is represented using a basis function expansion which reflects the most relevant (or measurable) features of the signal. This model of neural activity leads naturally to a Bayesian likelihood function which balances the model fit to the data with the complexity of the model, where the complexity is related to the number of included events. A novel Expectation-Maximization algorithm which maximizes the likelihood function is presented. The new method is shown to be effective on several MEG simulations of neurological activity as well as data from a self-paced finger tapping experiment.