Consistent Estimation of the FMRI Hemodynamic Response Function in AR(1) Noise

Different approaches have been considered so far for nonparametric Hemodynamic Response Function (HRF) estimation in noisy functional Magnetic Resonance Imaging (fMRI). However, very few methods have considered the temporal correlation of the fMRI times series when estimating the HRF as most of these methods use a Gaussian white noise model. In this paper, this issue is addressed by modeling the noise in fMRI times series by an autoregressive model of order one (AR(1)). Making use of a semiparametric model to characterize the fMRI time series and the AR(1) to model the temporally correlated noise, a generalized least squares estimator for voxelwise consistent non-parametric HRF estimation is derived in this paper. The proposed error structure estimation method has the advantage of not involving any nonparametric estimation. The effectiveness of the proposed HRF estimation procedure is illustrated on both simulated and experimental fMRI data from a finger tapping experiment.