Inverse problem (source estimation)

The EEG/MEG inverse problem is the estimation of the neural sources that produced an observed set of sensor signals. It is fundamentally ill-posed: Helmholtz showed in the nineteenth century that a given exterior field can be produced by infinitely many interior source configurations, so the mapping from data to sources is non-unique. It is also ill-conditioned (small measurement noise can produce large errors in the estimate) and underdetermined (far more candidate sources than sensors).

Because the data alone cannot select a solution, every inverse method must impose additional assumptions — priors or constraints — to obtain a unique, stable estimate. These range from parametric assumptions (a small number of point dipoles) to distributed priors (minimum energy, spatial smoothness, sparsity) to spatial-filtering formulations (beamformers). The choice of prior, not the data, largely determines the character of the solution, so an inverse result must always be interpreted in light of its assumptions.