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. In this talk, I will briefly define some key properties of the discrete wavelet transform (DWT) and review its applications to statistical analysis of fMRI data, focusing on: i) time series resampling by "wavestrapping" of wavelet coefficients; ii) methods for efficient linear model estimation in the context of long memory or 1/f-like noise; and iii) wavelet based methods for multiple hypothesis testing.
For more backgound information please see recent review by Bullmore et al (2003) "Wavelets and statistical analysis of functional magnetic resonance images of the human brain" Statistical Methods in Medical Research vol 12 (in press), and references therein. This work was supported by a Human Brain Project grant from the National Institute of Biomedical Imaging and Bioengineering and the National Institute of Mental Health.
Continuous wavelet transform of fractal fMRI time series
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