Modeling the haemodynamic response in fMRI using smooth FIR filters

Modeling the haemodynamic response in functional magnetic resonance (fMRI) experiments is an important aspect of the analysis of functional neuroimages. This has been done in the past using parametric response function, from a limited family. In this contribution, we adopt a semi-parametric approach based on finite impulse response (FIR) filters. In order to cope with the increase in the number of degrees of freedom, we introduce a Gaussian process prior on the filter parameters. We show how to carry on the analysis by incorporating prior knowledge on the filters, optimizing hyper-parameters using the evidence framework, or sampling using a Markov Chain Monte Carlo (MCMC) approach. We present a comparison of our model with standard haemodynamic response kernels on simulated data, and perform a full analysis of data acquired during an experiment involving visual stimulation.