Ozcan Alpay
Biomedical MR Laboratory, Mallinckrodt Institute of Radiology, Washington University in Saint Louis, School of Medicine, Box 8227, St. Louis, MO 63110, USA.
Annu Int Conf IEEE Eng Med Biol Soc. 2009;2009:2707-10. doi: 10.1109/IEMBS.2009.5333395.
The linear algebra framework for MR-DTI introduced in the companion manuscript is expanded to a normed space structure. The issues originating from the inclusion of imaging gradients into the MR-DTI model to obtain a fuller description are tackled by the optimization theory. A sample independent, geometric objective function based on matrix norms is defined. A parametrization of feasible diffusion gradient sets is presented so that the optimization can be carried out by making sure that the coefficient matrix for the estimation equations has full rank. The experiments are carried with the optimal gradient schemes. There are significant improvements in terms of model matching error and the lowering of the difference between eigenvalues calculated with or without the imaging gradients.
配套论文中介绍的用于磁共振扩散张量成像（MR-DTI）的线性代数框架被扩展为赋范空间结构。通过优化理论解决了将成像梯度纳入MR-DTI模型以获得更全面描述时产生的问题。定义了一个基于矩阵范数的样本独立几何目标函数。提出了可行扩散梯度集的参数化方法，以便通过确保估计方程的系数矩阵具有满秩来进行优化。使用最优梯度方案进行实验。在模型匹配误差以及降低有无成像梯度时计算的特征值之间的差异方面有显著改进。
