Numerical Studies of Recovery Chances for a Simplified EIT Problem

Abstract

This study investigates a simplified discretized EIT model with eight electrodes distributed equally spaced at the boundary of a disc covered with a small number of material ‘stripes’ of varying conductivity. The goal of this paper is to evaluate the chances of identifying the conductivity values of each stripe from rotating measurements of potential differences. This setting comes from an engineering background, where the used EIT model is exploited for the detection of conductivities in carbon nanotubes (CNT) and carbon nanofibers (CNF). Connections between electrical conductivity and mechanical strain have been of major interest within the engineering community and has motivated the investigation of such a ‘stripe’ structure. Up to five conductivity values can be recovered from noisy 8 × 8 data matrices in a stable manner by a least squares approach. Hence, this is a version of regularization by discretization and additional tools for stabilizing the recovery seem to be superfluous. To our astonishment, no local minima of the squared misfit functional were observed, which seems to indicate uniqueness of the recovery if the number of stripes is quite small.