Sparse estimation of the hemodynamic response functionin functional near infrared spectroscopy

Functional near-infrared spectroscopy (fNIRS) signals offer an interesting alternative to functional magnetic resonance imaging (fMRI) when investigating the temporal dynamics of brain region responses during activations. The hemodynamic response function (HRF) is the object of primary interest to neuroscientists in this case. Making use of a semiparametric model to characterize the oxygenated (HbO) and deoxygenated (HbR) fNIRS time-series and a sparsity assumption on the HRF, a new method for non-parametric HRF estimation from a single fNIRS signal is derived in this paper. The proposed method consistently estimates the HRF using a profile least square estimator obtained using the local polynomial smoothing technique applied to estimate the drift and introducing a regularization penalty in the minimization problem to promote sparsity of the HRF coefficients. The performance of the proposed method is assessed on both simulated and fNIRS data from a finger tapping experiment.