Reconstruction of unknown cavity by single measurement

TL;DR

This paper introduces a novel domain sampling reconstruction method for identifying unknown cavities within a medium using only a single boundary measurement, adapting the no response test for inverse boundary problems.

Contribution

It extends the single NRT method to inverse boundary value problems, enabling cavity detection with minimal measurement data.

Findings

Successfully reconstructs unknown cavities from single boundary measurements.

Adapts the no response test for inverse boundary value problems.

Provides a new approach for minimal measurement inverse problems.

Abstract

In this paper we propose a domain sampling type reconstruction scheme for an inverse boundary value problem to identify an unknown cavity by single measurement on the accessible boundary of a known electric or heat conductive medium. Here the single measurement is to give single current or heat flux which can have a small support over the boundary, and we measure the corresponding voltage or temperature over the whole boundary. For this inverse boundary value problem, we adapted the single NRT (no response test) introduced by Luke and Potthast for inverse scattering problem and show that it can provide such a domain sampling type reconstruction scheme.