Nonnegative Definite EAP and ODF Estimation via a Unified Multi-Shell HARDI Reconstruction

Jian Cheng (1, 2) , Tianzi Jiang (3) , Rachid Deriche (2)

1 NLPR - National Laboratory of Pattern Recognition [Beijing]
2 ATHENA - Computational Imaging of the Central Nervous System
3 National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, PR China

In High Angular Resolution Diffusion Imaging (HARDI), Orientation Distribution Function (ODF) and Ensemble Average Propagator (EAP) are two important Probability Density Functions (PDFs) which reflect the water diffusion and fiber orientations. Spherical Polar Fourier Imaging (SPFI) is a recent model-free multi-shell HARDI method which estimates both EAP and ODF from the diffusion signals with multiple b values. As physical PDFs, ODFs and EAPs are nonnegative definite respectively in their domains S^2 and R^3 . However, existing ODF / EAP estimation methods like SPFI seldom consider this natural constraint. Although some works considered the nonnegative constraint on the given discrete samples of ODF / EAP, the estimated ODF/EAP is not guaranteed to be nonnegative definite in the whole continuous domain. The Riemannian framework for ODFs and EAPs has been proposed via the square root parameterization based on pre-estimated ODFs and EAPs by other methods like SPFI. However, there is no work on how to estimate the square root of ODF / EAP called as the wavefuntion directly from diffusion signals. In this paper, based on the Riemannian framework for ODFs / EAPs and Spherical Polar Fourier (SPF) basis representation, we propose a unified model-free multi-shell HARDI method, named as Square Root Parameterized Estimation (SRPE), to simultaneously estimate both the wavefunction of EAPs and the nonnegative definite ODFs and EAPs from diffusion signals. The experiments on synthetic data and real data showed SRPE is more robust to noise and has better EAP reconstruction than SPFI, especially for EAP profiles at large radius.

Domaines: Imagerie médicale

Jian Cheng, Tianzi Jiang, Rachid Deriche. Nonnegative Definite EAP and ODF Estimation via a Unified Multi-Shell HARDI Reconstruction. Medical Image Computing and Computer-Assisted Intervention - MICCAI 2012, Oct 2012, Nice, France. pp.313-321, ⟨10.1007/978-3-642-33418-4_39⟩. ⟨hal-00759014⟩