Traditional methods to analyze image data from PET, MRI and fMRI have proven only partially successful. This is due in part to the inherent biological variability, physical limitations of the acquisition instrumentation, and mathematical algorithms applied to reconstruct the image data, but it also reflects the inadequacy of the computational, mathematical, and statistical methods employed in analysis of these data. Image data acquired by PET and MRI have numerous sources of distortion. Depending on the imaging modality, these appear as spatial distortions, decreases in signal-to-noise ratio, modification of image values, and increased spatial correlation. PET and MRI data can be """"""""improved"""""""" by using appropriate models to restore and analyze the reconstructed image. Methods in both the spatial domain, using the theory of Gaussian random fields and Fourier or frequency domain have being developed for analysis of PET and fMRI. In order to evaluate these models, simulated PET brain intensity data and PET and MRI brain shape data have been created using empirically measured image characteristics for PET and MRI. In particular, Monte Carlo techniques have been developed to create groups of PET data with known attributes and specific group differences. The control of signal and noise associated with these models allows us to evaluate the effect of geometric distortions and sensitivity of identification of localized statistically significant differences between the groups. In the case of geometric models it is possible to create 3-D brain (or skull) shapes with known noise to evaluate the limitations of rescaling of PET images across subjects to a given standard and registration of MRI and PET images for the same subject. These simulations are being used to study two related areas currently under investigation: (1) statistical techniques are being researched for both the geometric and grey scale values of PET and MRI data; and (2) the precision of multimodality 3-D superposition of functional and structural images obtained for PET and MRI data especially when the data are sparse or have known symmetries.
