McGraw Tim, Vemuri Baba, Özarslan Evren, Chen Yunmei, Mareci Thomas
West Virginia University, Morgantown, WV 26506, USA.
University of Florida, Gainesville, FL 32601, USA.
Inverse Probl Imaging (Springfield). 2009 Nov;3(4):625-648. doi: 10.3934/ipi.2009.3.625.
In this paper, we present a novel variational formulation for restoring high angular resolution diffusion imaging (HARDI) data. The restoration formulation involves smoothing signal measurements over the spherical domain and across the 3D image lattice. The regularization across the lattice is achieved using a total variation (TV) norm based scheme, while the finite element method (FEM) was employed to smooth the data on the sphere at each lattice point using first and second order smoothness constraints. Examples are presented to show the performance of the HARDI data restoration scheme and its effect on fiber direction computation on synthetic data, as well as on real data sets collected from excised rat brain and spinal cord.
在本文中，我们提出了一种用于恢复高角分辨率扩散成像（HARDI）数据的新型变分公式。该恢复公式涉及在球域和三维图像格点上对信号测量值进行平滑处理。格点上的正则化是通过基于总变差（TV）范数的方案实现的，而有限元方法（FEM）则用于在每个格点处利用一阶和二阶平滑约束对球面上的数据进行平滑处理。文中给出了示例，以展示HARDI数据恢复方案的性能及其对合成数据以及从切除的大鼠脑和脊髓收集的真实数据集上纤维方向计算的影响。
