A Kullback-Leibler Methodology for HRF Estimation in fMRI Data
Hemodynamic Response Function (HRF) estimation in functional Magnetic Resonance Imaging (fMRI) experiments is an important issue in functional neuroimages analysis. Indeed, when modeling each brain region as a stationary linear system characterized by its impulse response, the HRF describes the temporal dynamic of the brain region response during activations. Using the mixed-effects model, a new algorithm for maximum likelihood HRF estimation is derived. In this model, the random effect is used to better account for the variability of the drift. Contrary to the usual approaches, the proposed algorithm has the benefit of considering an unknown drift matrix. Estimations of the HRF and the hyperparameters are derived by alternating minimization of the Kullback-Leibler divergence between a model family of probability distributions defined using the mixed-effects model and a desired family of probability distributions constrained to be concentrated on the observed data. The relevance of proposed approach is demonstrated both on simulated and real data.
Keywords: HRF estimation, Kullback-Leibler divergence