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A Riemannian Framework for Ensemble Average Propagator Computing

Jian Cheng 1, 2, * Aurobrata Ghosh 1 Tianzi Jiang 2 Rachid Deriche 1 
* Corresponding author
1 ATHENA - Computational Imaging of the Central Nervous System
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In Diffusion Tensor Imaging (DTI), Riemannian framework (RF) [1] has been proposed for processing tensors, which is based on Information Geometry theory. Many papers have shown that RF is useful in tensor estimation, interpolation, smoothing, regularization, segmentation and so on. Recently RF also has been proposed for Orientation Distribution Function (ODF) computing [2,3] and it is applicable to any Probability Density Function (PDF) based on any orthonormal basis representation. Spherical Polar Fourier Imaging (SPFI) [4,5] was proposed recently to fast and robustly estimate the ODF and Ensemble Average Propagator (EAP) from arbitrary sampled DWI signals. 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.
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Submitted on : Friday, August 19, 2011 - 9:13:15 AM
Last modification on : Saturday, June 25, 2022 - 11:06:32 PM
Long-term archiving on: : Sunday, December 4, 2016 - 2:18:20 PM


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  • HAL Id : inria-00615436, version 1
  • PRODINRA : 246167



Jian Cheng, Aurobrata Ghosh, Tianzi Jiang, Rachid Deriche. A Riemannian Framework for Ensemble Average Propagator Computing. ISMRM, May 2011, Montréal, Canada. ⟨inria-00615436⟩



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