Year: 2024
Type: article
Abstract: This work solves the three-dimensional inverse boundary value problem with the quadratic Wasserstein distance (W 2), which originates from the optimal transportation (OT) theory. The computation of the W 2 distance on the manifold surface is boiled down to solving the generalized Monge–Ampère equation, whose solution is directly related to the gradient of the W 2 distance. An efficient first-order method based on iteratively solving Poisson’s equation is introduced to solve the fully nonlinear elliptic equation. Combining with the adjoint-state technique, the optimization framework based on the W 2 distance is developed to solve the three-dimensional electrical impedance tomography problem. The proposed method is especially suitable for severely ill-posed and highly nonlinear inverse problems. Numerical experiments demonstrate that our method improves the stability and outperforms the traditional regularization methods.
Source: Inverse Problems
Authors: Gang Bao, Yixuan Zhang
Institutions: Zhejiang University, Peking University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Awards: G1552893609, G2943700727, G6755039076
OpenAlex ID: W4403628662