Wang Z, Vemuri B C, Chen Y, Mareci T
Department of Computer & Information Sciences & Engr, University of Florida, Gainesville, FL 32611, USA.
Inf Process Med Imaging. 2003 Jul;18:660-71. doi: 10.1007/978-3-540-45087-0_55.
In this paper, we present a novel constrained variational principle for simultaneous smoothing and estimation of the diffusion tensor field from diffusion weighted imaging (DWI). The constrained variational principle involves the minimization of a regularization term in an LP norm, subject to a nonlinear inequality constraint on the data. The data term we employ is the original Stejskal-Tanner equation instead of the linearized version usually employed in literature. The original nonlinear form leads to a more accurate (when compared to the linearized form) estimated tensor field. The inequality constraint requires that the nonlinear least squares data term be bounded from above by a possibly known tolerance factor. Finally, in order to accommodate the positive definite constraint on the diffusion tensor, it is expressed in terms of cholesky factors and estimated. variational principle is solved using the augmented Lagrangian technique in conjunction with the limited memory quasi-Newton method. Both synthetic and real data experiments are shown to depict the performance of the tensor field estimation algorithm. Fiber tracts in a rat brain are then mapped using a particle system based visualization technique.
在本文中，我们提出了一种新颖的约束变分原理，用于从扩散加权成像（DWI）同时平滑和估计扩散张量场。该约束变分原理涉及在LP范数下最小化一个正则项，并受数据上的非线性不等式约束。我们采用的数据项是原始的斯捷克卡尔 - 坦纳方程，而不是文献中通常使用的线性化版本。原始的非线性形式能得到更准确（与线性化形式相比）的张量场估计。不等式约束要求非线性最小二乘数据项由一个可能已知的容差因子从上方界定。最后，为了适应扩散张量的正定约束，它用乔列斯基因子表示并进行估计。使用增广拉格朗日技术结合有限内存拟牛顿法求解变分原理。合成数据和真实数据实验都展示了张量场估计算法的性能。然后使用基于粒子系统的可视化技术绘制大鼠脑中的纤维束。
