Wavelet-Based Estimation of Hemodynamic Response Function

We present a new algorithm to estimate hemodynamic response function (HRF) and drift component in wavelet domain. The HRF is modeled as a gaussian function with unknown parameters. The functional Magnetic resonance Image (fMRI) noise is modeled as a fractional brownian motion (fBm). The HRF parameters are estimated in wavelet domain since wavelet transform with sufficient number of vanishing moments decorrelates a fBm process. Due to this decorrelating property of wavelet transform, the noise covariance matrix in wavelet domain can be assumed to be diagonal whose entries are estimated using sample variance estimators at each scale. We study the influence of sampling time and shape assumption on the estimation performance. Results are presented by adding synthetic HRFs on null fMRI data.