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Optimal Transportation for Electrical Impedance Tomography (2210.16082v1)

Published 28 Oct 2022 in math.NA, cs.NA, math-ph, and math.MP

Abstract: This work establishes a framework for solving inverse boundary problems with the geodesic based quadratic Wasserstein distance ($W_{2}$). A general form of the Fr\'echet 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.

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