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Statistical Methods in Medical Research, Vol. 12, No. 5, 375-399 (2003)
DOI: 10.1191/0962280203sm339ra

Wavelets and statistical analysis of functional magnetic resonance images of the human brain

Ed Bullmore

Brain Mapping Unit and Wolfson Brain Imaging Centre, University of Cambridge, Addenbrooke’s Hospital, Cambridge, UK and Institute of Psychiatry, King’s College London, London, UK

Jalal Fadili

GREYC CNRS UMR 6072, Caen, France

Michael Breakspear

Brain Dynamics Centre (Westmead Hospital) and School of Physics, University of Sydney, Australia

Raymond Salvador

Brain Mapping Unit and Wolfson Brain Imaging Centre, University of Cambridge, Addenbrooke’s Hospital, Cambridge, UK

John Suckling

Brain Mapping Unit and Wolfson Brain Imaging Centre, University of Cambridge, Addenbrooke’s Hospital, Cambridge, UK

Michael Brammer

Institute of Psychiatry, King’s College London, London, UK, m.brammer{at}iop.kcl.ac.uk

Wavelets provide an orthonormal basis for multiresolution analysis and decorrelation or ‘whitening’ of nonstationary time series and spatial processes. Wavelets are particularly well suited to analysis of biological signals and images, such as human brain imaging data, which often have fractal or scale-invariant properties. We briefly define some key properties of the discrete wavelet transform (DWT) and review its applications to statistical analysis of functional magnetic resonance imaging (fMRI) data. We focus on time series resampling by ‘wavestrapping’ of wavelet coefficients, methods for efficient linear model estimation in the wavelet domain, and wavelet-based methods for multiple hypothesis testing, all of which are somewhat simplified by the decorrelating property of the DWT.


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