Grouping a few sets of normally distributed voxels of SPECT volumes in discrimination between Alzheimer dementia and controls

It is widely accepted and can be easily verified that any specific voxel in a class of brain single photon emission computed tomography (SPECT) volumes is of a univariate normal distribution. In this research, we conjecture that all the voxels in a class of SPECT volumes are also approximately of a multivariate normal (MVN) distribution from which in terms of the Bayes errors of statistics, an optimal classifier can be designed using quadratic discriminant functions (QDFs). However, the number of training volumes needed for deriving the covariance matrix of an MVN distribution increases quadratically with respect to the number of voxels such that practically the MVN distributions cannot be modeled. To overcome this, we selected a reduced number of voxels and put them into groups based on the P values of two-sided t tests or a greedy algorithm of discrimination between two classes of volumes. We also tried the same approach on the 3D Haar wavelet coefficients which were obtained from the discrete wavelet transform of the voxels. Experiments showed that the accuracies of QDFs, linear discriminant functions (LDFs), and support vector machines (SVMs) were not significantly different in discrimination between Alzheimer´s and normal controls verifying that the proposed MVNs effectively model the discrimination information. Moreover, the proposed QDF classifier obtained satisfactory performance.