Consistent hemodynamic response function estimation in functional MRI by first order differencing

Non-parametric hemodynamic response function (HRF) estimation in noisy functional Magnetic Resonance Imaging (fMRI) plays an important role when investigating the temporal dynamic of a brain region response during activations. Assuming the drift Lipschitz continuous; a new algorithm for non-parametric HRF estimation is derived in this paper. The proposed algorithm estimates the HRF by applying a first order differencing to the fMRI time series samples. It is shown that the proposed HRF estimator is √(N) consistent. Its performance is assessed using both simulated and a real fMRI data sets obtained from an event-related fMRI experiment. The application results reveal that the proposed HRF estimation method is efficient both computationally and in term of accuracy.