Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT

TL;DR

This paper introduces a shape optimization algorithm for electrical impedance tomography that reconstructs piecewise constant conductivities on polygonal partitions, demonstrating robustness and accuracy through numerical simulations.

Contribution

It presents a novel shape derivative-based method for EIT reconstruction of piecewise constant conductivities on polygonal partitions.

Findings

Robustness demonstrated in simulated tests

High accuracy in boundary reconstruction

Effective in two-dimensional cases

Abstract

In this paper, we develop a shape optimization-based algorithm for the electrical impedance tomography (EIT) problem of determining a piecewise constant conductivity on a polygonal partition from boundary measurements. The key tool is to use a distributed shape derivative of a suitable cost functional with respect to movements of the partition. Numerical simulations showing the robustness and accuracy of the method are presented for simulated test cases in two dimensions.