Forward model (forward problem)

The forward model is the computation of the sensor signals that a given source configuration would produce, given a head geometry and its conductivities. Under the quasi-static approximation it is linear in the source amplitudes, so it can be written as a matrix — the lead field — that maps source dipole moments to channel measurements. Solving it requires a source space (candidate locations and orientations), a volume-conductor model (geometry plus conductivities), and a sensor description.

The forward problem is well-posed and, given an accurate head model, essentially exact up to numerical error — in stark contrast to the inverse problem. Every inverse method, from dipole fitting to beamforming, is built on top of a forward model, so forward-model error (wrong skull conductivity, coarse mesh, imprecise sensor coregistration) propagates directly into localization error. Accurate forward modelling is therefore the foundation on which all source estimates stand.