Estimation of Spontaneous Neuronal Activity Using Homomorphic Filtering

Blood Oxygen Level-Dependent (BOLD) signal changes in functional magnetic resonance imaging (fMRI) measures neuronal activities blurred by hemodynamic response function (HRF) and hence may not be reliable to estimate functional connectivity (FC). Several methods have been attempted to estimate the neuronal activity signal (NAS) from the observed BOLD signal. Using this as a blind source separation problem, these methods assume a parametric model of HRF. But it is not clear if these models accurately reflect the biophysical process. In this paper, we have proposed an approach based on a homomorphic filter (HMF) to deconvolve NAS from resting state fMRI (rs-fMRI) time course. It exploits the hypothesis that the HRF has predominantly low frequency energy in comparison to the NAS. Hence, by choosing an appropriate value of cutoff quefrency with the help of thresholded BOLD signal after HMF, HRF can be suppressed from observed BOLD signal to get an estimate of NAS. The estimated NAS, in the framework of dictionary learning (DL), is able to produce subtle resting state networks (RSNs) in comparison with the existing blind deconvolution (BD) method. The Jaccard similarity distance between RSNs by taking random samples and the entire subjects underpins the robustness of the estimated RSNs. Another quantitative comparison has also been drawn to show the efficacy of the HMF in the estimation of NAS using the maximum normalized cross-correlation coefficient (MNCC) distribution for different RSNs.