Extreme diffusion values for non-Gaussian diffusions

A new magnetic resonance imaging (MRI) model, called diffusion kurtosis imaging (DKI), was recently proposed, to characterize the non-Gaussian diffusion behaviour in tissues. DKI involves a fourth-order three-dimensional tensor and a second-order three-dimensional tensor. Similar to those in the diffusion tensor imaging (DTI) model, the extreme diffusion values and extreme directions associated to this tensor pair play important roles in DKI. In this paper, we study the properties of the extreme values and directions associated to such tensor pairs. We also present a numerical method and its preliminary computational results.