Statistical methods in the Fourier domain to enhance and classify images

A mathematical model, for which rigorous methods of statistical inference are available, is described and techniques for image enhancement and linear discriminant analysis of groups are developed. Since the gray values of neighboring pixels in tomographically produced medical images are spatially correlated, the calculations are carried out in the Fourier domain to insure statistical independence of the variables. Furthermore, to increase the power of statistical tests the known spatial covariance was used to specify constraints in the spectral domain. These methods were compared to statistical procedures carried out in the spatial domain. Positron emission tomography (PET) images of alcoholics with organic brain disorders were compared by these techniques to age-matched normal volunteers. Although these techniques are employed to analyze group characteristics of functional images, they provide a comprehensive set of mathematical and statistical procedures in the spectral domain that can also be applied to images of other modalities, such as computed tomography (CT) or magnetic resonance imaging (MRI).