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.
Joint work with Arthur Toga (UCLA, Neurology), Michael Mega (Neural Net Research), and John Boscardin (UCLA, Biostatistics).
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