One-step iterative reconstruction of conductivity inclusion via the concept of topological derivative

TL;DR

This paper introduces a one-step iterative algorithm for locating small conductivity inhomogeneities inside a conductor using boundary measurements, based on the topological derivative concept in Electrical Impedance Tomography.

Contribution

It develops a novel one-step iterative method utilizing topological derivatives for efficient localization of small inclusions in EIT.

Findings

Algorithm successfully locates small conductivity inhomogeneities.

Numerical experiments demonstrate the feasibility of the proposed method.

Abstract

We consider an inverse problem of location identification of small conductivity inhomogeneity inside a conductor via boundary measurements which occurs in the EIT (Electrical Impedance Tomography). For this purpose, we derive topological derivative by applying the asymptotic formula for steady state voltage potentials in the existence of conductivity inclusion of small diameter. Using this derivative, we design only one-step iterative location search algorithm of small conductivity inhomogeneity completely embedded in the homogeneous domain by solving an adjoint problem. Numerical experiments presented for showing the feasibility of proposed algorithm.