  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.
