Barmpoutis Angelos, Vemuri Baba C, Forder John R
The University of Florida, Gainesville Department of CISE - Department of Radiology Gainesville, Florida 32611.
Proc IEEE Int Symp Biomed Imaging. 2008 May 14;5:911-914. doi: 10.1109/ISBI.2008.4541145.
Cartesian tensor basis have been widely used to approximate spherical functions. In Medical Imaging, tensors of various orders have been used to model the diffusivity function in Diffusion-weighted MRI data sets. However, it is known that the peaks of the diffusivity do not correspond to orientations of the underlying fibers and hence the displacement probability profiles should be employed instead. In this paper, we present a novel representation of the probability profile by a 4(th) order tensor, which is a smooth spherical function that can approximate single-fibers as well as multiple-fiber structures. We also present a method for efficiently estimating the unknown tensor coefficients of the probability profile directly from a given high-angular resolution diffusion-weighted (HARDI) data set. The accuracy of our model is validated by experiments on synthetic and real HARDI datasets from a fixed rat spinal cord.
笛卡尔张量基已被广泛用于近似球函数。在医学成像中，各种阶数的张量已被用于对扩散加权磁共振成像（MRI）数据集中的扩散函数进行建模。然而，众所周知，扩散率的峰值并不对应于潜在纤维的方向，因此应采用位移概率分布。在本文中，我们提出了一种用四阶张量表示概率分布的新方法，它是一种光滑的球函数，可以近似单纤维和多纤维结构。我们还提出了一种直接从给定的高角分辨率扩散加权（HARDI）数据集有效估计概率分布未知张量系数的方法。我们通过对来自固定大鼠脊髓的合成和真实HARDI数据集进行实验，验证了我们模型的准确性。
