Optimal Transportation for Electrical Impedance Tomography

10/28/2022

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by   Gang Bao, et al.

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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 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.