Li Changyou, Yu Wenwei, Huang Shao Ying
School of Electronics and Information, Northwestern Polytechnical University, China.
Center for Frontier Medical Engineering, Chiba University, Japan; and.
Tomography. 2017 Mar;3(1):50-59. doi: 10.18383/j.tom.2016.00283.
Here, a method based on viscosity-type regularization is proposed for magnetic resonance electrical property tomography (MREPT) to mitigate persistent artifacts when it is used to reconstruct a map of electrical properties based on data from a magnetic resonance imaging scanner. The challenges for solving the corresponding partial differential equation (PDE) are discussed in detail. The existing artifacts in the numerical results are pointed out and classified. The methods in the literature for MREPT are mainly based on an assumption of local homogeneity, which makes the approach simple but leads to artifacts in the transition region where electrical properties vary rapidly. Recent work has focused on eliminating the assumption of local homogeneity, and one of the solutions is convection-reaction MREPT that is based on a first-order PDE. Numerical solutions of the PDE have persistent artifacts in certain regions and global spurious oscillations. Here, a method based on viscosity-type regularization is proposed to effectively mitigate the aforementioned problems. Finite difference method is used for discretizing the governing PDE. Numerical experiments are presented to analyze the problem in detail. Electrical properties of different phantoms are successfully retrieved. The efficiency, accuracy, and noise tolerance of the proposed method are illustrated with numerical results.
本文提出了一种基于粘性型正则化的方法用于磁共振电阻抗断层成像（MREPT），以减轻在利用磁共振成像扫描仪的数据重建电特性图时出现的持续伪影。详细讨论了求解相应偏微分方程（PDE）所面临的挑战。指出并分类了数值结果中存在的现有伪影。文献中用于MREPT的方法主要基于局部均匀性假设，这使得方法简单，但在电特性快速变化的过渡区域会产生伪影。近期工作集中在消除局部均匀性假设，其中一种解决方案是基于一阶PDE的对流反应MREPT。PDE的数值解在某些区域存在持续伪影和全局虚假振荡。在此，提出一种基于粘性型正则化的方法来有效减轻上述问题。采用有限差分法对控制PDE进行离散化。给出了数值实验以详细分析该问题。成功反演了不同体模的电特性。数值结果说明了所提方法的效率、准确性和噪声容限。
