Nonparametric Hemodynamic Deconvolution of fMRI Using Homomorphic Filtering

Functional magnetic resonance imaging (fMRI) is an indirect measure of neural activity which is modeled as a convolution of the latent neuronal response and the hemodynamic response function (HRF). Since the sources of HRF variability can be nonneural in nature, the measured fMRI signal does not faithfully represent underlying neural activity. Therefore, it is advantageous to deconvolve the HRF from the fMRI signal. However, since both latent neural activity and the voxel-specific HRF is unknown, the deconvolution must be blind. Existing blind deconvolution approaches employ highly parameterized models, and it is unclear whether these models have an over fitting problem. In order to address these issues, we 1) present a nonparametric deconvolution method based on homomorphic filtering to obtain the latent neuronal response from the fMRI signal and, 2) compare our approach to the best performing existing parametric model based on the estimation of the biophysical hemodynamic model using the Cubature Kalman Filter/Smoother. We hypothesized that if the results from nonparametric deconvolution closely resembled that obtained from parametric deconvolution, then the problem of over fitting during estimation in highly parameterized deconvolution models of fMRI could possibly be over stated. Both simulations and experimental results demonstrate support for our hypothesis since the estimated latent neural response from both parametric and nonparametric methods were highly correlated in the visual cortex. Further, simulations showed that both methods were effective in recovering the simulated ground truth of the latent neural response.