Linearization Error in Electrical Impedance Tomography

In electromagnetic tomography and resistivity survey a linearized model approximation is often used, in the context of regularized regression, to image the conductivity distribution in a domain of interest. Due to the error introduced by the simplified model, quantitative image reconstruction becomes challenging unless the conductivity is sufficiently close to a constant. We derive a closed form expression of the linearization error in electrical impedance tomography based on the complete electrode model. The error term is expressed in an integral form involving the gradient of the perturbed electric potential and renders itself readily available for analytical or numerical computation. For real isotropic conductivity changes with piecewise uniform characteristic functions the perturbed potential field can be shown to satisfy Poisson's equation with Robin boundary conditions and interior point sources positioned at the interfaces of the inhomogeneities. Simulation experiments using a finite element method have been performed to validate these results.