Medical Image Analysis Laboratory, School of Computing Science, Simon Fraser University, Burnaby, BC, Canada.
Med Image Anal. 2012 Aug;16(6):1121-9. doi: 10.1016/j.media.2012.07.002. Epub 2012 Jul 25.
A novel method for estimating a field of fiber orientation distribution (FOD) based on signal de-convolution from a given set of diffusion weighted magnetic resonance (DW-MR) images is presented. We model the FOD by higher order Cartesian tensor basis using a parametrization that explicitly enforces the positive semi-definite property to the computed FOD. The computed Cartesian tensors, dubbed Cartesian Tensor-FOD (CT-FOD), are symmetric positive semi-definite tensors whose coefficients can be efficiently estimated by solving a linear system with non-negative constraints. Next, we show how to use our method for converting higher-order diffusion tensors to CT-FODs, which is an essential task since the maxima of higher-order tensors do not correspond to the underlying fiber orientations. Finally, we propose a diffusion anisotropy index computed directly from CT-FODs using higher order tensor distance measures thus consolidating the whole analysis pipeline of diffusion imaging solely using CT-FODs. We evaluate our method qualitatively and quantitatively using simulated DW-MR images, phantom images, and human brain real dataset. The results conclusively demonstrate the superiority of the proposed technique over several existing multi-fiber reconstruction methods.
本文提出了一种基于给定的一组扩散加权磁共振（DW-MR）图像进行信号解卷积来估计纤维方向分布（FOD）场的新方法。我们使用参数化方法通过高阶笛卡尔张量基对 FOD 进行建模，该参数化方法明确地将正半定性质施加到计算出的 FOD 上。所计算的笛卡尔张量，称为笛卡尔张量-FOD（CT-FOD），是对称正定半张量，其系数可以通过求解具有非负约束的线性系统来有效地估计。接下来，我们展示了如何使用我们的方法将高阶扩散张量转换为 CT-FOD，这是一项基本任务，因为高阶张量的最大值并不对应于潜在的纤维方向。最后，我们提出了一种直接从 CT-FOD 计算的扩散各向异性指数，使用高阶张量距离度量，从而仅使用 CT-FOD 整合扩散成像的整个分析管道。我们使用模拟 DW-MR 图像、体模图像和人脑真实数据集对我们的方法进行了定性和定量评估。结果明确证明了所提出的技术优于几种现有的多纤维重建方法。
