What and where in electromagnetic brain imaging

To understand the brain, we may record electromagnetic signals and use them to infer the dynamics of brain activity (the "what"), and the location or distribution of its sources within the brain (the "where"). In this paper, these two aspects emerge from the experimental data via distinct analysis pathways. In a first step, recordings of brain activity undergo linear data-driven analysis that results in an analysis matrix, the first column of which isolates a source of interest. In a second step, the remaining columns of the analysis matrix are used to estimate the position of the source, with the help of a source model informed by the anatomical scans and sensor geometry. Specifically, each column is interpreted as a null filter for the source of interest (a spatial filter that suppresses that source). Each such null filter admits a zero set, or subset of the source parameter space for which the filter output is zero. Since the source of interest is necessarily within the zero sets of all of its null filters, its location can be found by taking the intersection of these zero sets. There is no theoretical limit to location accuracy, but practical limits may arise from noise in the data, imperfect calibration, or an incomplete or inaccurate source model. The method is illustrated with simulated and real data.