Semi-blind deconvolution of neural impulse response in fMRI using a Gibbs sampling method

In functional magnetic resonance imaging (fMRI), the hemodynamic response function (HRF) represents the impulse response of the neurovascular system. Its identification is essential for a better understanding of cerebral activity since it provides a typical time course of the response to a stimulus in a given region of interest (ROI). The authors have developed an HRF estimation method based on a single time course (Ciuciu, P. et al., IEEE Trans. Medical Imaging, vol.22, no.10, p.1235-51, 2003). We now propose an extension that takes the spatial homogeneity of the HRF into account. Our hypothesis, based on biological results, is that a ROI can be characterized by a single HRF but varying magnitude in space. Our goal is to estimate those magnitudes that could then be interpreted as a correlate of the neural response. We are thus faced with a semi-blind deconvolution inverse problem since the time arrivals of the neural response are known - they correspond to stimuli timing. To cope with this issue, we introduce specific prior information about the HRF and the neural response. Finally, we develop an MCMC approach to approximate the posterior mean estimates of unknown quantities. Simulation results show the improvement brought by our formulation compared to our earlier approach.