Cheng Jian, Ghosh Aurobrata, Deriche Rachid, Jiang Tianzi
Center for Computational Medicine, LIAMA, Institute of Automation, Chinese Academy of Sciences, China.
Med Image Comput Comput Assist Interv. 2010;13(Pt 1):648-56. doi: 10.1007/978-3-642-15705-9_79.
High Angular Resolution Imaging (HARDI) can better explore the complex micro-structure of white matter compared to Diffusion Tensor Imaging (DTI). Orientation Distribution Function (ODF) in HARDI is used to describe the probability of the fiber direction. There are two type definitions of the ODF, which were respectively proposed in Q-Ball Imaging (QBI) and Diffusion Spectrum Imaging (DSI). Some analytical reconstructions methods have been proposed to estimate these two type of ODFs from single shell HARDI data. However they all have some assumptions and intrinsic modeling errors. In this article, we propose, almost without any assumption, a uniform analytical method to estimate these two ODFs from DWI signals in q space, which is based on Spherical Polar Fourier Expression (SPFE) of signals. The solution is analytical and is a linear transformation from the q-space signal to the ODF represented by Spherical Harmonics (SH). It can naturally combines the DWI signals in different Q-shells. Moreover It can avoid the intrinsic Funk-Radon Transform (FRT) blurring error in QBI and it does not need any assumption of the signals, such as the multiple tensor model and mono/multi-exponential decay. We validate our method using synthetic data, phantom data and real data. Our method works well in all experiments, especially for the data with low SNR, low anisotropy and non-exponential decay.
与扩散张量成像（DTI）相比，高角分辨率成像（HARDI）能够更好地探索白质的复杂微观结构。HARDI中的方向分布函数（ODF）用于描述纤维方向的概率。ODF有两种类型的定义，分别是在Q球成像（QBI）和扩散谱成像（DSI）中提出的。已经提出了一些解析重建方法来从单壳HARDI数据估计这两种类型的ODF。然而，它们都有一些假设和内在的建模误差。在本文中，我们几乎在没有任何假设的情况下，提出了一种统一的解析方法，用于从q空间中的扩散加权成像（DWI）信号估计这两种ODF，该方法基于信号的球极傅里叶表达式（SPFE）。该解决方案是解析的，是从q空间信号到由球谐函数（SH）表示的ODF的线性变换。它可以自然地组合不同Q壳中的DWI信号。此外，它可以避免QBI中固有的Funk-Radon变换（FRT）模糊误差，并且不需要对信号进行任何假设，例如多张量模型和单/多指数衰减。我们使用合成数据、体模数据和真实数据验证了我们的方法。我们的方法在所有实验中都表现良好，特别是对于低信噪比、低各向异性和非指数衰减的数据。
