A UNIFIED FRAMEWORK FOR ESTIMATING DIFFUSION TENSORS OF ANY ORDER WITH SYMMETRIC POSITIVE-DEFINITE CONSTRAINTS.
A UNIFIED FRAMEWORK FOR ESTIMATING DIFFUSION TENSORS OF ANY ORDER WITH SYMMETRIC POSITIVE-DEFINITE CONSTRAINTS.
复制标题
一个统一的框架，用于估计具有对称正定约束的任何顺序的扩散张量。
DOI：
10.1109/isbi.2010.5490256
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发表时间：
2010-04-14
期刊：
影响因子：
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通讯作者：
Vemuri BC
中科院分区：
文献类型：
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作者：
Barmpoutis A;Vemuri BC
各种阶数的笛卡尔张量已被用于在扩散加权MRI数据集中对扩散率或取向分布函数进行建模。在这两种情况下，估计张量必须是正定的，因为它们模拟正值函数。在本文中，我们提出了一个新的统一框架，估计正定张量的任何顺序，在文献中，这是特定的顺序或未能处理正定性质的现有方法相比。建议的框架采用了齐次多项式参数化，覆盖了整个空间的任何阶正定张量，并明确施加正定约束的估计张量。我们表明，这种参数化导致一个线性系统，使用非负最小二乘技术解决。该框架证明使用合成和真实的数据从切除的大鼠海马。
Cartesian tensors of various orders have been employed for either modeling the diffusivity or the orientation distribution function in Diffusion-Weighted MRI datasets. In both cases, the estimated tensors have to be positive-definite since they model positive-valued functions. In this paper we present a novel unified framework for estimating positive-definite tensors of any order, in contrast to the existing methods in literature, which are either order-specific or fail to handle the positive-definite property. The proposed framework employs a homogeneous polynomial parametrization that covers the full space of any order positive-definite tensors and explicitly imposes the positive-definite constraint on the estimated tensors. We show that this parametrization leads to a linear system that is solved using the non-negative least squares technique. The framework is demonstrated using synthetic and real data from an excised rat hippocampus.