Non-white noise in fMRI: does modelling have an impact?

The sources of non-white noise in Blood Oxygenation Level Dependent (BOLD) functional magnetic resonance imaging (fMRI) are many. Familiar sources include low-frequency drift due to hardware imperfections, oscillatory noise due to respiration and cardiac pulsation and residual movement artefacts not accounted for by rigid body registration. These contributions give rise to temporal autocorrelation in the residuals of the fMRI signal and invalidate the statistical analysis as the errors are no longer independent. The low-frequency drift is often removed by high-pass filtering, and other effects are typically modelled as an autoregressive (AR) process. In this paper, we propose an alternative approach: Nuisance Variable Regression (NVR). By inclusion of confounding effects in a general linear model (GLM), we first confirm that the spatial distribution of the various fMRI noise sources is similar to what has already been described in the literature. Subsequently, we demonstrate, using diagnostic statistics, that removal of these contributions reduces first and higher order autocorrelation as well as non-normality in the residuals, thereby improving the validity of the drawn inferences. In addition, we also compare the performance of the NVR method to the whitening approach implemented in SPM2.