title: Wavelets and functional magnetic resonance imaging of the human brain.
abstract: The discrete wavelet transform (DWT) is widely used for multiresolution analysis and decorrelation or "whitening" of nonstationary time series and spatial processes. Wavelets are naturally appropriate for analysis of biological data, such as functional magnetic resonance images of the human brain, which often demonstrate scale invariant or fractal properties. We provide a brief formal introduction to key properties of the DWT and review the growing literature on its application to fMRI. We focus on three applications in particular: (i) wavelet coefficient resampling or "wavestrapping" of 1-D time series, 2- to 3-D spatial maps and 4-D spatiotemporal processes; (ii) wavelet-based estimators for signal and noise parameters of time series regression models assuming the errors are fractional Gaussian noise (fGn); and (iii) wavelet shrinkage in frequentist and Bayesian frameworks to support multiresolution hypothesis testing on spatially extended statistic maps. We conclude that the wavelet domain is a rich source of new concepts and techniques to enhance the power of statistical analysis of human fMRI data.
authors.affiliation: Brain Mapping Unit and Wolfson Brain Imaging Centre, University of Cambridge, Addenbrooke's Hospital, Cambridge, UK. etb23@cam.ac.uk
authors.forename: Ed
authors.initials: E
authors.lastname: Bullmore
authors.forename: Jalal
authors.initials: J
authors.lastname: Fadili
authors.forename: Voichita
authors.initials: V
authors.lastname: Maxim
authors.forename: Levent
authors.initials: L
authors.lastname: Sendur
authors.forename: Brandon
authors.initials: B
authors.lastname: Whitcher
authors.forename: John
authors.initials: J
authors.lastname: Suckling
authors.forename: Michael
authors.initials: M
authors.lastname: Brammer
authors.forename: Michael
authors.initials: M
authors.lastname: Breakspear
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D001921:Brain / Q000033:anatomy & histology*; D005189:False Positive Reactions; D006801:Humans; D007091:Image Processing, Computer-Assisted; D008279:Magnetic Resonance Imaging; D008959:Models, Neurological; D016011:Normal Distribution; D010100:Oxygen / Q000097:blood; D018709:Statistics, Nonparametric; D009626:Terminology as Topic
chemical_list: D010100:Oxygen