Simplified reconstruction of layered materials in EIT

TL;DR

This paper presents a simplified method for reconstructing layered conductivities in electrical impedance tomography, removing the need for bounds and reducing complexity using monotonicity theory.

Contribution

It introduces a streamlined reconstruction approach that simplifies previous methods by eliminating the need for bounds and reducing computational complexity.

Findings

Simplifies layered conductivity reconstruction process.

Removes the need for a priori bounds on conductivities.

Uses monotonicity-based theory to reduce complexity.

Abstract

This short note considerably simplifies a reconstruction method by the author (Comm. PDE, 45(9):1118--1133, 2020), for reconstructing piecewise constant layered conductivities (PCLC) from partial boundary measurements in electrical impedance tomography. Theory from monotonicity-based reconstruction of extreme inclusions eliminates most of the bookkeeping related to multiple components of each layer, and also simplifies the involved test operators. Moreover, the method no longer requires a priori lower and upper bounds to the unknown conductivity values.