Lead field

The lead field is the linear operator that encodes the forward model: its column for a given source is the vector of sensor signals produced by a unit dipole at that location and orientation. Stacking columns for all candidate sources gives the lead-field (or gain) matrix L, so that measured data x relate to source amplitudes s by x = L s + noise. By the reciprocity theorem, a sensor's lead field can equivalently be read as the sensitivity field one would compute by driving a unit current through that sensor.

Because the number of candidate sources vastly exceeds the number of sensors, L is a wide matrix with a large null space — the mathematical origin of the inverse problem's non-uniqueness. The structure of the lead field (smooth, spatially overlapping columns) also explains why deep and radial sources are poorly resolved: their columns have small norm or are nearly collinear with those of other sources, so the data barely constrain them.