Consistent hemodynamic response estimation function in fMRI using sparse prior information

Non-parametric Hemodynamic Response Function (HRF) estimation in noisy functional Magnetic Resonance Imaging (fMRI) plays an important role when investigating the temporal dynamics of regional brain responses during activation. Making use of a semiparametric model to characterize the fMRI time series and a sparsity assumption on the HRF, a new method for voxelwise non-parametric HRF estimation is derived in this paper. The proposed method consistently estimates the HRF by applying first order differencing to the fMRI time series samples and introducing a regularization penalty in the minimization problem to promote sparsity of the HRF coefficients. Based on the likelihood ratio test (LRT) principle, a new statistical test for detecting activated pixels is proposed using the estimated HRF. The effectiveness of the HRF estimation method is illustrated on both simulated and experimental fMRI data from a visual experiment.