Uniqueness and Lipschitz stability in Electrical Impedance Tomography with finitely many electrodes
For the EIT community, this provides theoretical guarantees for nonlinear reconstruction with practical electrode models, though the result is incremental as it extends existing linearized theory.
This paper extends uniqueness and Lipschitz stability results for Electrical Impedance Tomography with the Complete Electrode Model from the linearized to the full nonlinear case, showing that finitely many electrodes uniquely determine piecewise-analytic conductivities in finite-dimensional subspaces.
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.