Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography

TL;DR

This paper introduces a monotonicity-based regularization method for shape reconstruction in electrical impedance tomography, effectively handling noise and model errors, and demonstrating accurate detection and characterization of inhomogeneities.

Contribution

It develops a new regularization scheme for monotonicity-based shape reconstruction applicable to practical measurement models, including the complete electrode model.

Findings

Successfully detects inhomogeneities under regularization

Achieves asymptotic exact shape characterization

Demonstrates effectiveness on simulated and real data

Abstract

The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it was shown that a simple monotonicity property of the related Neumann-to-Dirichlet map can be used to characterize shapes of inhomogeneities in a known background conductivity. In this paper we formulate a monotonicity-based shape reconstruction scheme that applies to approximative measurement models, and regularizes against noise and modelling error. We demonstrate that for admissible choices of regularization parameters the inhomogeneities are detected, and under reasonable assumptions, asymptotically exactly characterized. Moreover, we rigorously associate this result with the complete electrode model, and describe how a computationally cheap monotonicity-based reconstruction algorithm can be implemented. Numerical reconstructions from both simulated and real-life measurement data are presented.