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 magnetic resonance imaging (MRI) and fMRI to empirically estimate the distribution of the wavelet coefficients of the data both across individuals and spatial locations. An anatomical subvolume probabilistic atlas is used to tessellate the structural and functional signals into smaller regions each of what 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 on all the regions are computed in a compressed wavelet space. These are modeled by heavy-tail distributions because their histograms exhibit slower tail decay than the Gaussian. We discovered that the 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 dataset involving repeated presentation of sensory-motor response stimuli young, elderly, and demented subjects.

In the field of template-based medical image analysis, image registration and normalization are frequently used to eval- uate and interpret data in a standard template or reference atlas space. Despite the large number of image-registration (warping) techniques developed recently in the literature, only a few studies have been undertaken to numerically characterize and compare various alignment methods. In this paper, we introduce a new approach for analyzing image registration based on a selective- wavelet reconstruction technique using a frequency-adaptive wavelet shrinkage. We study four polynomial-based and two higher complexity nonaffine warping methods applied to groups of stereotaxic human brain structural (magnetic resonance imaging) and functional (positron emission tomography) data. Depending upon the aim of the image registration, we present several warp classification schemes. Our method uses a concise representation of the native and resliced (pre- and post-warp) data in compressed wavelet space to assess quality of registration. This technique is com- putationally inexpensive and utilizes the image compression, image enhancement, and denoising characteristics of the wavelet-based function representation, as well as the optimality properties of frequency-dependent wavelet shrinkage.