An Integrated Framework for Joint HRF and Drift Estimation and HbO/HbR Signal Improvement in fNIRS Data

Nonparametric hemodynamic response function (HRF) estimation in functional near-infrared spectroscopy (fNIRS) data plays an important role when investigating the temporal dynamics of a brain region response during activations. Assuming the drift arising from both physical and physiological effects in fNIRS data is Lipschitz continuous; a novel algorithm for joint HRF and drift estimation is derived in this paper. The proposed algorithm estimates the HRF by applying a first-order differencing to the fNIRS time series samples in order to remove the drift effect. An estimate of the drift is then obtained using a wavelet thresholding technique applied to the residuals generated by removing the estimated induced activation response from the fNIRS time-series. It is shown that the proposed HRF estimator is √N consistent whereas the estimator of the drift is asymptotically optimal. The de-drifted fNIRS oxygenated (HbO) and deoxygenated (HbR) hemoglobin responses are then obtained by removing the corresponding estimated drifts from the fNIRS time-series. Its performance is assessed using both simulated and real fNIRS data sets. The application results reveal that the proposed joint HRF and drift estimation method is efficient both computationally and in terms of accuracy. In comparison to traditional model based methods used for HRF estimation, the proposed novel method avoids the selection of a model to remove the drift component. As a result, the proposed method finds an optimal estimate of the fNIRS drift and offers a model-free approach to de-drift the HbO/HbR responses.