Nonstationary noise estimation in functional MRI

An important issue in functional MRI analysis is accurate characterisation of the noise processes present in the data. Whilst conventional fMRI noise representations often assume stationarity (or time-invariance) in the noise generating sources, such approaches may serve to suppress important dynamic information about brain function. As an alternative to these fixed temporal assumptions, we present in this paper two time-varying procedures for examining nonstationary noise structure in fMRI data. In the first procedure, we approximate nonstationary behaviour by means of a collection of simple but numerous time-varying parametric models. This is accomplished through the derivation of a locally parametric AutoRegressive (AR) plus drift model which tracks temporal covariance by allowing the model parameters to evolve over time. Before exploring time variation in these parameters, window-widths (bandwidths) that are well suited to the latent time-varying noise structure must be determined. To do this, we employ a bandwidth selection mechanism based on Stein's Unbiased Risk Estimator (SURE) criterion. In the second procedure, we describe the fMRI noise using a nonparametric method based on Functional Data Analysis (FDA). This process generates well-conditioned nonstationary covariance estimates that reflect temporal continuity in the underlying data structure whilst penalizing effective model dimension. We demonstrate both methods on simulated data and investigate the presence of nonstationary noise in resting fMRI data using the whitening capabilities of the locally parametric procedure. We evaluate the comparative behaviour of the stationary and nonstationary AR-based methods on data acquired at 1.5, 3 and 7 T magnetic field strengths and show that incorporation of time variation in the AR parameters leads to an overall decrease in the level of residual structure in the data. The FDA noise modelling technique is formulated within an activation mapping procedure and compared to the SPM (Statistical Parametric Mapping) toolbox on a cognitive face recognition task. Both the SPM and FDA methods show good sensitivity on this task, but we find that inclusion of the nonstationary FDA noise model seems to improve detection power in important task-related medial temporal regions.