A Wavelet-Based Statistical Analysis
of fMRI data: I. Motivation and Data Distribution Modeling
Ivo D. Dinov1,2, John W. Boscardin3, Michael
S. Mega4 and Arthur W. Toga1
1Laboratory of Neuro Imaging, Department of Neurology, 2Department
of Statistics, 3Department of Biostatistics, UCLA, Los Angeles,
CA 90095. 4Pacific Health Research Institute, Honolulu, HI 96813.
Abstract
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.
Heavy-tail distributions are then proposed to model these data because these signals exhibit slower
tail decay than the Gaussian distribution. There are two basic directions we investigate in the first
part of this study: 1. Bayesian wavelet-based thresholding scheme, which allows better signal
representation, and; 2. A family of heavy-tail distributions, which are used as models for the real
MRI and fMRI timeseries data. 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. 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.