Statistical modeling of multimodal neuroimaging data in non-subsampled shearlet domain using the student's t location-scale distribution
Statistical modeling of high dimensional, correlated, and complex imaging data obtained from various longitudinal neuroimaging studies has become an inevitable part of automatic disease diagnosing tasks. In this paper, we propose a parametric brain image modeling based on the statistical properties of non-subsampled shearlet transform (NSST) coefficients. The NSST detail coefficients of multimodal neuroimaging data exhibit highly non-Gaussian property, i.e., the probability density function (PDF) of the NSST coefficients are sharply peaked around zero with heavy tails. As a consequence, the marginal statistics of the detail subband coefficients are modeled by student's t location-scale PDF, which has heavier tails (more prone to outliers) than the Gaussian distribution for smaller values of the shape parameter. The Jensen-Shannon divergence (JSD) goodness-of-fit shows that the detail NSST subbands of neuroimaging data in the longitudinal Alzheimer's disease neuroimaging initiative database are well approximated by student's t location-scale distribution compared to that by the traditional generalized Gaussian distribution.