Estimating Smoothness in Statistical Parametric Maps

Abstract

The smoothness parameter that characterises the spatial dependence of pixel values in functional brain images is usually estimated empirically from the data. Since this parameter is essential for the assessment of significant changes in brain activity, it is important to know (a) the variance of its estimator and (b) how this variability affects the results of the ensuing statistical analysis. In this article, we derive an approximate expression for the variance of the smoothness estimator and investigate the effects of this variability on assessing the significance of cerebral activation in statistical parametric maps using a verbal fluency PET activation experiment. Our results suggest that, for p values around 0.05, the variability in the p value (due to smoothness estimation) is approximately 20%. The effect of the assessment of the spatial dependency of the data is far from being negligible, and this suggests a more comprehensive methodology for functional imaging than the one used so far. This work provides a simple tool for taking into account this effect.