Integral Curve Estimation for High Angular Resolution Diffusion Imaging
Lyudmila Sakhanenko, Department of Statistics & Probability, Michigan State University, USA
High Angular Resolution Diffusion Imaging is a vivo brain imaging technique that allows to understand axonal anatomy. However, the images have a notoriously high level of noise. We model the uncertainty in images via a super-tensor model, where the components of a diffusion super-tensor are the slopes in a system of regression equations that are measured by a MRI scanner. Then we study how the uncertainty propagates from the tensor field to a vector field to the integral curves, which serve as the models for axonal fibers. We construct the estimators of the fibers, show their asymptotical normality, and develop computationally fast tractography approach. As a result, brain images are enhanced via confidence tubes enveloping the estimated fibers that quantify and picture the uncertainty present in the data. The location of fibers and their connectivity are important to neuroscientists, since aging and some diseases such as Alzheimer's change how the brain regions connect to each other.