论文标题
电阻断层扫描的最佳运输
Optimal Transportation for Electrical Impedance Tomography
论文作者
论文摘要
这项工作建立了一个框架，用于解决基于测量的二次瓦斯坦距离（$ w_ {2} $）的逆边界问题。 Fréchet梯度的一般形式是通过最佳运输（OT）理论系统地得出的。此外，开发了基于$ \ mathbb {s}^{1} $的新公式的快速算法，以解决相应的最佳传输问题。从$ O（N^{3}）$的传统方法的算法的计算复杂性降低至$ O（n）$。与伴随状态方法相结合，该框架提供了一种新的计算方法来解决具有挑战性的电阻抗层析成像（EIT）问题。提出了数值示例，以说明我们方法的有效性。
This work establishes a framework for solving inverse boundary problems with the geodesic based quadratic Wasserstein distance ($W_{2}$). A general form of the Fréchet gradient is systematically derived by optimal transportation (OT) theory. In addition, a fast algorithm based on the new formulation of OT on $\mathbb{S}^{1}$ is developed to solve the corresponding optimal transport problem. The computational complexity of the algorithm is reduced to $O(N)$ from $O(N^{3})$ of the traditional method. Combining with the adjoint-state method, this framework provides a new computational approach for solving the challenging electrical impedance tomography (EIT) problem. Numerical examples are presented to illustrate the effectiveness of our method.
