主 题: Higher Order Positive Semi-Definite Diffusion Tensor Imaging and Space Tensor Conic Programming
报告人: Prof. Liqun Qi (The Hong Kong Polytechnic University )
时 间: 2009-09-09 下午16:00 - 17:30
地 点: 理科一号楼 1568
Due to the well-known limitations of diffusion tensor imaging (DTI),
high angular resolution diffusion imaging (HARDI) is used to
characterize non-Gaussian diffusion processes. One approach to
analyze HARDI data is to model the apparent diffusion coefficient
(ADC) with higher order diffusion tensors (HODT). The diffusivity
function is positive semi-definite. In the literature, some
methods have been proposed to preserve positive semi-definiteness of
second order and fourth order diffusion tensors. None of them can
work for arbitrary high order diffusion tensors. In this paper, we
propose a comprehensive model to approximate the ADC profile by a
positive semi-definite diffusion tensor of either second or higher
order. We call this model PSDT (positive semi-definite diffusion
tensor). 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.
Performance of PSDT is depicted on synthetic data as well as MRI
data.
PSDT can also be regarded as a conic linear programming (CLP) problem.
Yinyu Ye and I investigated PSDT from the viewpoint of CLP. We
characterize
the dual cone of the positive semi-definite space tensor cone, and study
the
CLP formulation and duality of the positive semi-definite space tensor
programming (STP) problem.
