Jiao Fangxiang, Gur Yaniv, Johnson Chris R, Joshi Sarang
SCI Institute, University of Utah, Salt Lake City, UT 84112, USA.
Inf Process Med Imaging. 2011;22:538-49. doi: 10.1007/978-3-642-22092-0_44.
Fundamental to high angular resolution diffusion imaging (HARDI), is the estimation of a positive-semidefinite orientation distribution function (ODF) and extracting the diffusion properties (e.g., fiber directions). In this work we show that these two goals can be achieved efficiently by using homogeneous polynomials to represent the ODF in the spherical deconvolution approach, as was proposed in the Cartesian Tensor-ODF (CT-ODF) formulation. Based on this formulation we first suggest an estimation method for positive-semidefinite ODF by solving a linear programming problem that does not require special parameterization of the ODF. We also propose a rank-k tensor decomposition, known as CP decomposition, to extract the fibers information from the estimated ODF. We show that this decomposition is superior to the fiber direction estimation via ODF maxima detection as it enables one to reach the full fiber separation resolution of the estimation technique. We assess the accuracy of this new framework by applying it to synthetic and experimentally obtained HARDI data.
高角分辨率扩散成像（HARDI）的基础是估计正定方向分布函数（ODF）并提取扩散特性（例如纤维方向）。在这项工作中，我们表明，正如笛卡尔张量ODF（CT - ODF）公式中所提出的那样，通过在球面反卷积方法中使用齐次多项式来表示ODF，可以有效地实现这两个目标。基于此公式，我们首先通过解决一个线性规划问题，提出了一种正定ODF的估计方法，该方法不需要对ODF进行特殊参数化。我们还提出了一种秩-k张量分解，即CP分解，以从估计的ODF中提取纤维信息。我们表明，这种分解优于通过ODF最大值检测进行的纤维方向估计，因为它能够达到估计技术的全纤维分离分辨率。我们通过将这个新框架应用于合成的和实验获得的HARDI数据来评估其准确性。
