Theoretical Analysis and Practical Insights on EAP Estimation via a Unified HARDI Framework

Jian Cheng 1, 2, * Tianzi Jiang 1 Rachid Deriche 2
* Corresponding author
2 ATHENA - Computational Imaging of the Central Nervous System
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Since Diffusion Tensor Imaging (DTI) cannot describe complex non-Gaussian diffusion process, many techniques, called as single shell High Angular Resolution Diffusion Imaging (sHARDI) methods, reconstruct the Ensemble Average Propagator (EAP) or its feature Orientation Distribution Function (ODF) from diffusion weighted signals only in single shell. Q-Ball Imaging (QBI) and Diffusion Orientation Transform (DOT) are two famous sHARDI methods. However, these sHARDI methods have some intrinsic modeling errors or need some unreal assumptions. Moreover they are hard to deal with signals from different q-shells. Most recently several novel multiple shell HARDI (mHARDI) methods, including Diffusion Propagator Imaging (DPI), Spherical Polar Fourier Imaging (SPFI) and Simple Harmonic Oscillator based Reconstruction and Estimation (SHORE), were proposed to analytically estimate EAP or ODF from multiple shell (or arbitrarily sampled) signals. These three methods all represent diffusion signal with some basis functions in spherical coordinate and use plane wave formula to analytically solve the Fourier transform. To our knowledge, there is no theoretical analysis and practical comparison among these sHARDI and mHARDI methods. In this paper, we propose a unified computational framework, named Analytical Fourier Transform in Spherical Coordinate (AFT-SC), to perform such theoretical analysis and practical comparison among all these five state-of-the-art diffusion MRI methods. We compare these five methods in both theoretical and experimental aspects. With respect to the theoretical aspect, some criteria are proposed for evaluation and some differences together with some similarities among the methods are highlighted. Regarding the experimental aspect, all the methods are compared in synthetic, phantom and real data. The shortcomings and advantages of each method are highlighted from which SPFI appears to be among the best because it uses an orthonormal basis that completely separates the spherical and radial information.
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Jian Cheng, Tianzi Jiang, Rachid Deriche. Theoretical Analysis and Practical Insights on EAP Estimation via a Unified HARDI Framework. MICCAI Workshop on Computational Diffusion MRI (CDMRI), Sep 2011, Toronto, Canada. ⟨inria-00615430⟩

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