The aim of this project is the development of statistical methods that either take into account interpixel correlation, or apply global image transform methods that permit an analysis of uncorrelated image components. Of typical interest is the investigation of differences between either images from individual subjects acquired under different experimental conditions, or between average images of subjects from different diagnostic groups. Three different statistical methods have been developed, based on the Fourier transform, the wavelet transform, and the theory of Gaussian random fields in the spatial domain. In the Fourier domain, the statistics at different wave numbers are uncorrelated and inference tests can be performed unencumbered by spatial correlations. This method provides for rigorous statistical tests with well-known properties and interpretations, but results in spatially uniform image blurring and may yield relatively poor spatial localization. For the wavelet-transform based analysis, a mathematically rigorous theory has been established that applies parametric statistical tests on wavelet coefficients and results in estimates of local image differences by inverse wavelet transform of only significant coefficients. The method provides for good spatial localization and the implementation of locally adaptive image smoothing, but there has not been much experience accumulated for the interpretation of test outcomes and estimates of image differences. Gaussian random field analysis has good spatial localization properties and permits the investigation of correlations with external variables (e.g., age), but it results in spatially uniform image blurring and does not provide for statistically reconstructed estimates of images differences (either across group or conditions). All three methods have been applied to the analysis of PET images from normal and alcoholic subjects and have identified significant differences in generally the same brain regions. Gaussian random field analysis was able to demonstrate in PET images from alcoholics a significant negative correlation of glucose utilization in the pre-frontal cortex with age. Current research on these topics includes the development of a 1-D Gaussian random field method to analyze fMRI time series data. This methodology can be used to analyze fMRI data acquired from experiments designed to incorporate a long (that is long enough, as determined experimentally, to estimate the variance associated with the acquired data) baseline condition and transition to another activated state. It uses the long baseline data to estimate the variance measure associated with the temporal data from a voxel within the image and sets a statistically rigorous threshold for activation in spite of the known temporal correlation in the data. This analysis technique is being validated with simulated and experimental data. Furthermore, this analysis technique is being incorporated into numerous experiments including one designed to look at the blood flow changes in the brain associated with alcoholic intake in normal subjects. This presents an ideal demonstration of this analysis technique to basically establish a response curve for alcohol intake. Finally, statistical analysis in the temporal domain based on traditional time series analysis in the Fourier domain have been developed and given similar results in terms of localization of the signal in fMRI blood flow studies to other less rigorous and generalizable techniques. This analysis methodology has the potential to (1) localize fMRI activation changes, (2) estimate or reconstruct the activated signal without the associated noise, (3) estimate the hemodynamic response function locally without prior assumptions as to its structure, and (4) detect multiple responses to multiple input stimuli. Currently this technique is being used to study both simple finger tap data as well as more complex experimental designs.
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