Efficient Regularization of Temporal Autocorrelation Estimates in fMRI Data

摘要

Temporal autocorrelation present in functional magnetic resonance (fMR) images affects their statistical analysis. Pre-whitening is thus performed on fMRI data, generally with a first order autoregressive, i.e., AR(1) model implemented to estimate the temporal autocorrelations. Spatial smoothing filter is then normally applied to regularize these autocorrelation estimates, in order to reduce their variance, before using them in an REML process to perform pre-whitening. Some researchers have found that smoothing these autocorrelation estimates with spatial smoothing filters prevents the successful modeling of negatively correlated and approximately white spectra. Smoothing was also found to result in underestimation of positive correlations when weakly correlated or white spectral residuals bordered these positively correlated residuals. In our proposed method, we apply random field analysis based regularization, with a modified conditional random field, rather than a smoothing filter. It provides the necessary reduction in variance of AR(1) coefficients by taking into account the neighborhood autocorrelation estimates and at the same time preserves the borders between the positive, negative and white spectral residuals.