Optimal transportation for electrical impedance tomography

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS ACS Applied Bio Materials Pub Date : 2023-11-13 DOI:10.1090/mcom/3919

Gang Bao, Yixuan Zhang

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Abstract

This work establishes a framework for solving inverse boundary problems with the geodesic-based quadratic Wasserstein distance ( W 2 W_{2} ). A general form of the Fréchet gradient is systematically derived from the optimal transportation (OT) theory. In addition, a fast algorithm based on the new formulation of OT on S 1 \mathbb {S}^{1} is developed to solve the corresponding optimal transport problem. The computational complexity of the algorithm is reduced to O ( N ) O(N) from O ( N 3 ) 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 problem. Numerical examples are presented to illustrate the effectiveness of our method.

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电阻抗断层成像的最佳传输

本文建立了求解基于测地线的二次Wasserstein距离(w2w_{2})逆边界问题的框架。从最优运输理论出发，系统地导出了fr切特梯度的一般形式。此外，基于s1 \mathbb {S}^{1}上新的OT公式，提出了求解相应最优运输问题的快速算法。该算法的计算复杂度由传统方法的O(N 3) O(N^{3})降低到O(N) O(N)。结合伴随状态法，该框架为解决具有挑战性的电阻抗层析成像问题提供了一种新的计算方法。数值算例说明了该方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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