Information geometry and its application to theoretical statistics and diffusion tensor magnetic resonance imaging
Posted on:2011-10-19
Degree:Ph.D
Type:Thesis
University:University of California, Los Angeles
Candidate:Wisniewski, Nicholas Andrew
Full Text:PDF
GTID:2444390002464669
Subject:Applied Mathematics
Abstract/Summary:
This dissertation is divided into two parts. First we present an exact solution to a generalization of the Behrens-Fisher problem by embedding the problem in the Riemannian manifold of Normal distributions. From this we construct a geometric hypothesis testing scheme.;Secondly we investigate the most commonly used geometric methods employed in tensor field interpolation for DT-MRI analysis and cardiac computer modeling. We computationally investigate a class of physiologically motivated orthogonal tensor invariants, both at the full tensor field scale and at the scale of a single interpolation by doing a decimation/interpolation experiment. We show that Riemannian-based methods give the best results in preserving desirable physiological features.