Optimizing electrode positions in electrical impedance tomography

TL;DR

This paper develops a Bayesian-based method for optimally positioning electrodes in electrical impedance tomography to maximize the localization of the conductivity estimate, using linearization and gradient-based optimization.

Contribution

It introduces a novel gradient-based optimization approach for electrode placement in EIT, utilizing linearization of the forward model and explicit posterior covariance representation.

Findings

Effective electrode configurations improve conductivity localization.

The method reduces computational complexity via model linearization.

Numerical experiments validate the approach's practicality.

Abstract

This work considers finding optimal positions for the electrodes within the Bayesian paradigm based on available prior information on the conductivity; the aim is to place the electrodes so that the posterior density of the (discretized) conductivity, i.e., the conditional density of the conductivity given the measurements, is as localized as possible. To make such an approach computationally feasible, the complete electrode forward model of impedance tomography is linearized around the prior expectation of the conductivity, allowing explicit representation for the (approximate) posterior covariance matrix. Two approaches are considered: minimizing the trace or the determinant of the posterior covariance. The introduced optimization algorithm is of the steepest descent type, with the needed gradients computed based on appropriate Fr\'echet derivatives of the complete electrode model. The functionality of the methodology is demonstrated via two-dimensional numerical experiments.