A Wavelet-Based Statistical Analysis
of fMRI data: I. Motivation and Data Distribution Modeling
Ivo D. Dinov1,2, John W. Boscardin3, Michael
S. Mega4, Elizabeth L. Sowell1 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 these techniques
to analyze a large fMRI data set involving repeated presentation of sensory-motor
response stimuli in young, elderly and demented subjects.