首页> 外文会议>18th International Conference on Information Processing in Medical Imaging IPMI 2003 Jul 20-25, 2003 Ambleside, UK >A Constrained Variational Principle for Direct Estimation and Smoothing of the Diffusion Tensor Field from DWI
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A Constrained Variational Principle for Direct Estimation and Smoothing of the Diffusion Tensor Field from DWI

机译:DWI扩散张量场的直接估计和平滑的约束变分原理

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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 L~p 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.
机译:在本文中,我们提出了一种新的约束变分原理,用于同时进行扩散加权成像(DWI)的扩散张量场的平滑和估计。约束变分原理涉及到L〜p范数中的正则项的最小化,但要服从对数据的非线性不等式约束。我们使用的数据项是原始的Stejskal-Tanner方程,而不是文献中通常使用的线性化方程。原始的非线性形式导致更准确的(与线性化形式相比)估计的张量场。不等式约束要求非线性最小二乘数据项从上方受到可能已知的公差因子的限制。最后,为了适应对扩散张量的正定约束,以胆量因子表示并估计,使用增强拉格朗日技术结合有限记忆拟牛顿法求解了变分原理。合成和真实数据实验均显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大脑中的纤维束。

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