A Wavelet-Based Statistical Analysis of fMRI data: I

We propose a new method for statistical analysis of functional magnetic resonance imaging (fMRI) data. The discrete wavelet transformation is employed as a tool for efficient and robust signal representation. We use structural MRI and functional fMRI to empirically estimate the distribution of the wavelet coefficients of the data both across individuals and across spatial locations. An anatomical sub-volume probabilistic atlas is used to tessellate the structural and functional signals into smaller regions each of which is processed separately. A frequency-adaptive wavelet shrinkage scheme is employed to obtain essentially optimal estimations of the signals in the wavelet space. The empirical distributions of the signals are computed on all regions in compressed wavelet space. These are modeled by heavy-tail distributions because their histograms exhibit slower tail decay than the Gaussian. We discovered that Cauchy, Bessel K-Forms and Pareto distributions provide the most accurate asymptotic models for the distribution of the wavelet coefficients of the data. Finally, we propose a new model for statistical analysis of functional MRI data using this atlas-based wavelet-space representation. In the second part of our investigation we will apply this technique to analyze a large fMRI data set involving repeated presentation of sensory-motor response stimuli in young, elderly and demented subjects.