Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/6669
Title: Higher order positive semidefinite diffusion tensor imaging
Authors: Qi, L 
Yu, G
Wu, EX
Keywords: Positive semidefinite diffusion tensor
Apparent diffusion coefficient
Z-eigenvalue
Convex optimization problem
Invariants
Issue Date: 2010
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on imaging sciences, 2010, v. 3, no. 3, p. 416–433 How to cite?
Journal: SIAM Journal on imaging sciences 
Abstract: Due to the well-known limitations of diffusion tensor imaging, high angular resolution diffusion imaging (HARDI) is used to characterize non-Gaussian diffusion processes. One approach to analyzing HARDI data is to model the apparent diffusion coefficient (ADC) with higher order diffusion tensors. The diffusivity function is positive semidefinite. In the literature, some methods have been proposed to preserve positive semidefiniteness of second order and fourth order diffusion tensors. None of them can work for arbitrarily high order diffusion tensors. In this paper, we propose a comprehensive model to approximate the ADC profile by a positive semidefinite diffusion tensor of either second or higher order. We call this the positive semidefinite diffusion tensor (PSDT) model. PSDT is a convex optimization problem with a convex quadratic objective function constrained by the nonnegativity requirement on the smallest Z-eigenvalue of the diffusivity function. The smallest Z-eigenvalue is a computable measure of the extent of positive definiteness of the diffusivity function. We also propose some other invariants for the ADC profile analysis. Experiment results show that higher order tensors could improve the estimation of anisotropic diffusion and that the PSDT model can depict the characterization of diffusion anisotropy which is consistent with known neuroanatomy.
URI: http://hdl.handle.net/10397/6669
ISSN: 1936-4954 (online)
DOI: 10.1137/090755138
Rights: © 2010 Society for Industrial and Applied Mathematics
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