Determining conductivity and embedded obstacles from partial boundary measurements

TL;DR

This paper presents a method to simultaneously recover the conductivity distribution and embedded obstacles inside a domain using partial boundary measurements in Electrical Impedance Tomography, relying on PDE analysis and boundary data.

Contribution

It introduces a novel approach to recover both conductivity and obstacles from partial boundary data in EIT, extending previous methods that required full boundary measurements.

Findings

Simultaneous recovery of conductivity and obstacles from partial boundary data.

Use of coupled PDE-system and a priori estimates for harmonic functions.

Applicability to arbitrary small boundary subsets.

Abstract

In this paper, we consider an inverse conductivity problem on a bounded domain $\Omega\subset\mathbb{R}^n$, $n\geq2$, also known as Electrical Impedance Tomography (EIT), for the case where unknown impenetrable obstacles are embedded into $\Omega$. We show that a piecewise-constant conductivity function and embedded obstacles can be simultaneously recovered in terms of the local Dirichlet-to-Neumann map defined on an arbitrary small open subset of the boundary of the domain $\Omega$. The method depends on the well-posedness of a coupled PDE-system constructed for the conductivity equations in the $H^1$-space and some elementary a priori estimates for Harmonic functions.