On the Stability of Inverse Conductivity Problem for Polyhedral Inclusions under a Single Measurement

TL;DR

This paper establishes a logarithmic stability estimate for identifying convex polyhedral inclusions within a medium from a single boundary measurement, using advanced mathematical tools.

Contribution

It introduces a novel stability analysis for inverse conductivity problems involving polyhedral inclusions, combining singularity decomposition, propagation of smallness, and microlocal analysis.

Findings

Logarithmic stability estimate for Hausdorff distance between inclusions

Effective determination of convex polyhedral inclusions from single measurements

Application of microlocal analysis to inverse conductivity problems

Abstract

In this paper, we study the stability of the inverse conductivity problem of determining a convex polyhedral inclusion embedded in a homogeneous isotropic medium from a single boundary measurement. The main tools in our analysis are singularity decomposition for elliptic equations in non-smooth domains, propagation of smallness, and microlocal analysis. Combining these tools, we establish a logarithmic stability estimate for the Hausdorff distance between inclusions in terms of the measurement error.