Size estimates for the EIT problem with one measurement: the complex case

TL;DR

This paper develops bounds for estimating the size of an inclusion in a body using a single boundary measurement in the complex conductivity case, relevant for medical imaging applications.

Contribution

It introduces a method to estimate the volume of inclusions with boundary contact, using energy bounds and unique continuation estimates in the complex admittivity setting.

Findings

Established bounds for inclusion size based on power measurements.

Extended estimates to inclusions sharing boundary with the domain.

Provided quantitative unique continuation estimates for elliptic equations.

Abstract

In this paper we estimate the size of a measurable inclusion in terms of power measurements for a single applied boundary current. This problem arises in medical imaging for the screening of organs. For this kind of problem one has to deal mathematically with the complex conductivity (admittivity) equation. In this case we are able to establish, for certain classes of admittivities, lower and upper bounds of the measure of the inclusion in terms of the power measurements. A novelty of our result is that we are able to estimate also the volume of inclusions having part of its boundary in common with the reference body. Our analysis is based on the derivation of energy bounds and of fine quantitative estimates of unique continuation for solutions to elliptic equations.