Semi-blind deconvolution of neural impulse response in event-related fMRI using Gibbs sampler

Identification of the hemodynamic response function (HRF) in functional magnetic resonance imaging (fMRI) is essential for a better understanding of cerebral activity. In a given region-of-interest (ROI) of the brain, several works have demonstrated that neighbor voxels have close shape responses, but with potentially different magnitude. This property of similarity also holds between HRFs corresponding to different stimuli in the paradigm. In this paper, we account for these features in a given ROI and estimate a single HRF shape but several magnitude coefficients per voxel and condition, which may be thought of representing the neural response level. Identified as a semiblind deconvolution inverse problem, we use a Gibbs sampling approach to estimate the unknown quantities. Our method, validated both on synthetic and real fMRI data provides spatial activation maps in a given ROI with no assumptions on the exact shape of the HRF.