The Backus-Gilbert method [5,7,36] consists of finding an approximate inverse operator T of G that projects the EEG data M onto the solution space in such a way that the estimated primary current density D^BG = TM, is closest to the real primary current density inside the brain, in a least square sense. This is done by making the 1 × p vector RuvγT=TuγTGv (u, v = 1, 2, 3 and γ = 1, ..., p) as close as possible to δuvIγT where δ is the Kronecker delta and I γ is the γ th column of the p × p identity matrix. G v is a N × p matrix derived from G in such a way that in each row, only the elements in G corresponding to the vth direction are kept. The Backus-Gilbert method seeks to minimize the spread of the resolution matrix R, that is to maximize the resolving power. The generalized inverse matrix T optimizes, in a weighted sense, the resolution matrix.
