Normalisation

Although an individual voxel normalisation:

$$S_t(\ensuremath{\mathbf{x}}) = \frac{\sqrt{N_T} \, R_t(\ensu... ...T} R_t(\ensuremath{\mathbf{x}}) R_t(\ensuremath{\mathbf{x}})}}$$ (55)

can be used, the estimation of $V_0$ above effectively eliminates the need for normalisation.

However, this is only valid if the residual field is stationary, or at least approximately stationary. In this case, the variance is constant across all spatial points. If this is not the case, then the normalisation used by SPM (section 5.3) is more likely to produce a field that is a better approximation to a GRF.