Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/16355
Title: Nonnegative diffusion orientation distribution function
Authors: Qi, L 
Yu, G
Xu, Y
Keywords: High angular resolution diffusion imaging (HARDI)
Higher order diffusion tensor
Nonnegativity
Orientation distribution function (ODF)
Principal direction
Issue Date: 2013
Source: Journal of mathematical imaging and vision, 2013, v. 45, no. 2, p. 103-113 How to cite?
Journal: Journal of Mathematical Imaging and Vision 
Abstract: Because of the well-known limitations of diffusion tensor imaging (DTI) in regions of low anisotropy and multiple fiber crossing, high angular resolution diffusion imaging (HARDI) and Q-Ball Imaging (QBI) are used to estimate the probability density function (PDF) of the average spin displacement of water molecules. In particular, QBI is used to obtain the diffusion orientation distribution function (ODF) of these multiple fiber crossing. As a probability distribution function, the orientation distribution function should be nonnegative which is not guaranteed in the existing methods. This paper proposes a novel technique to guarantee the nonnegative property of ODF by solving a convex optimization problem, which has a convex quadratic objective function and a constraint involving the nonnega-tivity requirement on the smallest Z-eigenvalue of the diffusivity tensor. Using convex analysis and optimization techniques, we first derive the optimality conditions of this convex optimization problem. Then, we propose a gradient descent algorithm to solve this problem. We also present formulas for determining the principal directions (maxima) of the ODF. Numerical examples on synthetic data as well as MRI data are displayed to demonstrate the significance of our approach.
URI: http://hdl.handle.net/10397/16355
ISSN: 0924-9907
DOI: 10.1007/s10851-012-0346-y
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