Robust smoothness estimation in statistical parametric maps using standardized residuals from the general linear model

The assessment of significant activations in functional imaging using voxel-based methods often relies on results derived from the theory of Gaussian random fields. These results solve the multiple comparison problem and assume that the spatial correlation or smoothness of the data is known or can be estimated. End results (i.e., P values associated with local maxima, clusters, or sets of clusters) critically depend on this assessment, which should be as exact and as reliable as possible. In some earlier implementations of statistical parametric mapping (SPM) (SPM94, SPM95) the smoothness was assessed on Gaussianized t-fields (Gt-f) that are not generally free of physiological signal. This technique has two limitations. First, the estimation is not stable (the variance of the estimator being far from negligible) and, second, physiological signal in the Gt-f will bias the estimation. In this paper, we describe an estimation method that overcomes these drawbacks. The new approach involves estimating the smoothness of standardized residual fields which approximates the smoothness of the component fields of the associated t-field. Knowing the smoothness of these component fields is important because it allows one to compute corrected P values for statistical fields other than the t-field or the Gt-f (e.g., the F-map) and eschews bias due to deviation from the null hypothesis. We validate the method on simulated data and demonstrate it using data from a functional MRI study. (C) 1999 Academic Press.