Uniqueness and Lipschitz stability in Electrical Impedance Tomography with finitely many electrodes

TL;DR

This paper extends previous linearized results in Electrical Impedance Tomography to the full non-linear case, proving uniqueness and Lipschitz stability for finite-dimensional conductivities using finitely many electrodes.

Contribution

It generalizes the uniqueness and stability results from linearized to non-linear EIT, applicable to finite-dimensional subsets of piecewise-analytic functions.

Findings

Finitely many electrodes uniquely determine conductivities in finite-dimensional spaces.

Lipschitz stability of the reconstruction is established.

Results are extended to the continuum model with finite measurements.

Abstract

For the linearized reconstruction problem in Electrical Impedance Tomography (EIT) with the Complete Electrode Model (CEM), Lechleiter and Rieder (2008 Inverse Problems 24 065009) have shown that a piecewise polynomial conductivity on a fixed partition is uniquely determined if enough electrodes are being used. We extend their result to the full non-linear case and show that measurements on a sufficiently high number of electrodes uniquely determine a conductivity in any finite-dimensional subset of piecewise-analytic functions. We also prove Lipschitz stability, and derive analogue results for the continuum model, where finitely many measurements determine a finite-dimensional Galerkin projection of the Neumann-to-Dirichlet operator on a boundary part.