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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:


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.

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Next: Introduction