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Open Access Research article

Data-driven haemodynamic response function extraction using Fourier-wavelet regularised deconvolution

Alle Meije Wink1*, Hans Hoogduin2 and Jos BTM Roerdink23

Author Affiliations

1 Robert Steiner MR Unit, Imaging Sciences Department Imperial College, and MRC Clinical Sciences Centre, Hammersmith Hospital, London, UK

2 Institute for Behavioral and Cognitive Neurosciences and BCN Neuroimaging Center, Groningen, The Netherlands

3 Institute for Mathematics and Computing Science, University of Groningen, The Netherlands

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BMC Medical Imaging 2008, 8:7  doi:10.1186/1471-2342-8-7

Published: 10 April 2008



We present a simple, data-driven method to extract haemodynamic response functions (HRF) from functional magnetic resonance imaging (fMRI) time series, based on the Fourier-wavelet regularised deconvolution (ForWaRD) technique. HRF data are required for many fMRI applications, such as defining region-specific HRFs, effciently representing a general HRF, or comparing subject-specific HRFs.


ForWaRD is applied to fMRI time signals, after removing low-frequency trends by a wavelet-based method, and the output of ForWaRD is a time series of volumes, containing the HRF in each voxel. Compared to more complex methods, this extraction algorithm requires few assumptions (separability of signal and noise in the frequency and wavelet domains and the general linear model) and it is fast (HRF extraction from a single fMRI data set takes about the same time as spatial resampling). The extraction method is tested on simulated event-related activation signals, contaminated with noise from a time series of real MRI images. An application for HRF data is demonstrated in a simple event-related experiment: data are extracted from a region with significant effects of interest in a first time series. A continuous-time HRF is obtained by fitting a nonlinear function to the discrete HRF coeffcients, and is then used to analyse a later time series.


With the parameters used in this paper, the extraction method presented here is very robust to changes in signal properties. Comparison of analyses with fitted HRFs and with a canonical HRF shows that a subject-specific, regional HRF significantly improves detection power. Sensitivity and specificity increase not only in the region from which the HRFs are extracted, but also in other regions of interest.