Extracting the haemodynamic response function from fMRI time series using Fourier-wavelet regularised deconvolution with orthogonal spline wavelets

We describe a method to extract the haemodynamic response function (HRF) from functional magnetic resonance imaging (fMRI) time series based on Fourier-wavelet regularised deconvolution (ForWaRD), and introduce a simple model for the HRF. The HRF extraction algorithm extends the ForWaRD algorithm by introducing a more efficient computation in the case of very long wavelet filters. We compute shift-invariant discrete wavelet transforms (SIDWT) in the frequency domain, and apply ForWaRD using orthogonal spline wavelets. Extraction and modelling of subject-specific HRFs is demonstrated, as well as the use of these HRFs in a subsequent brain activation analysis. Temporal responses are predicted by using the extracted HRF coefficients. The resulting activation maps show the effectiveness of the proposed method.