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A linear and regularized ODF estimation algorithm to recover multiple fibers in Q-Ball imaging

Maxime Descoteaux 1 Elaine Angelino 1 Shaun Fitzgibbons 1 Rachid Deriche 1
1 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique de l'École normale supérieure, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : Due the well-known limitations of diffusion tensor imaging (DTI), high angular resolution diffusion imaging is currently of great interest to characterize voxels containing multiple fiber crossings. In particular, Q-ball imaging (QBI) is now a popular reconstruction method to obtain the orientation distribution function (ODF) of these multiple fiber distributions. The latter captures all important angular contrast by expressing the probability that a water molecule will diffuse into any given solid angle. However, QBI and other high order spin displacement estimation methods involve non-trivial numerical computations and lack a straightforward regularization process. In this paper, we propose a simple linear and regularized analytic solution for the Q-ball reconstruction of the ODF. First, the signal is modeled with a physically meaningful high order spherical harmonic series by incorporating the Laplace-Beltrami operator in the solution. This leads to an elegant mathematical simplification of the Funk-Radon transform using the Funk-Hecke formula. In doing so, we obtain a fast and robust model-free ODF approximation. We validate the accuracy of the ODF estimation quantitatively using the multi-tensor synthetic model where the exact ODF can be computed. We also demonstrate that the estimated ODF can recover known multiple fiber regions in a biological phantom and in the human brain. Another important contribution of the paper is the development of ODF sharpening methods. We show that sharpening the measured ODF enhances each underlying fiber compartment and considerably improves the extraction of fibers. The proposed techniques are simple linear transformations of the ODF and can easily be computed using our spherical harmonics machinery.
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Submitted on : Friday, May 19, 2006 - 7:40:29 PM
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Maxime Descoteaux, Elaine Angelino, Shaun Fitzgibbons, Rachid Deriche. A linear and regularized ODF estimation algorithm to recover multiple fibers in Q-Ball imaging. [Research Report] RR-5768, INRIA. 2005, pp.45. ⟨inria-00070253⟩

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