Deconvolution of neuronal signal from hemodynamic response

In this paper we describe a deconvolution technique for obtaining an approximation of the neuronal signal from an observed hemodynamic response in fMRI data. Our approach, based on the Rauch-Tung-Striebel smoother for square-root cubature Kalman filter, enables us to accurately infer the hidden states, parameters, and the input of the dynamic system. Using a series of simulations we show in this paper that we are able to move beyond the limitation of a poorly sampled observation signal and estimate the true structure of underlying neuronal signal with significantly improved temporal resolution.