Constrained Linear Basis Sets for HRF Modelling Using Variational Bayes
FMRIB Technical Report TR04MW2
(A related paper has been accepted for publication in Neuroimage)
Mark W. Woolrich, Timothy E.J. Behrens and Stephen M. Smith
Oxford Centre for Functional Magnetic Resonance Imaging of the Brain (FMRIB),
Department of Clinical Neurology, University of Oxford, John Radcliffe Hospital,
Headley Way, Headington, Oxford, UK
Corresponding author is Mark Woolrich:
woolrich@fmrib.ox.ac.uk
FMRI modelling requires flexible HRF modelling, with the HRF being
allowed to vary spatially and between subjects. To achieve this
flexibility, voxel-wise parameterised HRFs have been proposed,
however inference on such models is very slow. An alternative
approach is to use basis functions allowing inference to proceed
in the more manageable General Linear Model (GLM) framework.
However, a large amount of the subspace spanned by the basis
functions produces nonsensical HRF shapes. In this work we propose
a technique for choosing a basis set, and then the means to
constrain the subspace spanned by the basis set to only include
sensible HRF shapes.
Penny et al. (2003) showed how Variational Bayes
can be used to infer on the GLM for FMRI. Here we extend the work
of
Penny et al. (2003) to give inference on the GLM with
constrained HRF basis functions and
with spatial Markov Random Fields
on the autoregressive noise parameters.
Constraining the subspace spanned by the basis set
allows for far superior separation of activating voxels from
non-activating voxels in FMRI data. We use spatial mixture
modelling to produce final probabilities of activation and
demonstrate increased sensitivity on an FMRI dataset.
