Searching scale space for activation in PET images

PET images of cerebral blood flow (CBF) in an activation study are usually smoothed to a resolution much poorer than the intrinsic resolution of the PET camera. This is done to reduce noise and to overcome problems caused by neuroanatomic variability among different subjects undertaking the same experimental task. In many studies the choice of this smoothing is arbitrarily fixed at about 20 mm FWHM, and the resulting statistical field or parametric map is searched for local maxima. Poline and Mazoyer [(1994): J Cereb Blood Flow Metab 14:690-699; (1994): IEEE Trans Med Imaging 13(4):702-710] have proposed a 4-D search over smoothing kernel widths as well as the usual three spatial dimensions. If the peaks are well separated then this makes it possible to estimate the size of regions of activation as well as their location. One of the main problems identified by Poline and Mazoyer is how to assess the significance of scale space peaks. In this paper we provide a solution for the case of pooled-variance Z-statistic images (Gaussian fields). Our main result is a unified P value for the 4-D local maxima that is accurate for searches over regions of any shape or size. Our results apply equally well to any Gaussian statistical field, such as those resulting from fMRI.