A Riemannian Framework for Ensemble Average Propagator Computing

Jian Cheng^1,2, Aurobrata Ghosh¹, Tianzi Jiang², Rachid Deriche¹

In Diffusion Tensor Imaging (DTI), Riemannian framework (RF) has been proposed for processing tensors, which is based on Information Geometry theory. Recently RF also has been proposed for Orientation Distribution Function (ODF) computing. In this paper, we propose the RF for EAPs and implement it via SPFI. We proved that the RF for EAPs is diffeomorphism invariant, which is the natural extension of affine invariant RF for tensors. It could avoid the so-called swelling effect for interpolating EAPs, just like the RF for tensors. We also propose the Log-Euclidean framework (LEF), Affine-Euclidean framework (AEF), for fast processing EAPs, and Geometric Anisotropy (GA) for measuring the anisotropy of EAPs, which are all the extensions of previous concepts in RM for tensors respectively.