Simultaneous reconstruction of outer boundary shape and admittivity distribution in electrical impedance tomography

TL;DR

This paper presents a Newton-type algorithm that simultaneously reconstructs the shape and admittivity distribution of an object in electrical impedance tomography, reducing reliance on prior geometric information and improving reconstruction accuracy.

Contribution

The work introduces a novel method that jointly estimates object shape and admittivity, enhancing EIT reconstruction without requiring precise prior geometric data.

Findings

Successfully reconstructs shape and admittivity from simulated data

Demonstrates robustness to geometric uncertainties

Based on Fréchet derivative of the current-to-voltage map

Abstract

The aim of electrical impedance tomography is to reconstruct the admittivity distribution inside a physical body from boundary measurements of current and voltage. Due to the severe ill-posedness of the underlying inverse problem, the functionality of impedance tomography relies heavily on accurate modelling of the measurement geometry. In particular, almost all reconstruction algorithms require the precise shape of the imaged body as an input. In this work, the need for prior geometric information is relaxed by introducing a Newton-type output least squares algorithm that reconstructs the admittivity distribution and the object shape simultaneously. The method is built in the framework of the complete electrode model and it is based on the Fr\'echet derivative of the corresponding current-to-voltage map with respect to the object boundary shape. The functionality of the technique is demonstrated via numerical experiments with simulated measurement data.