A Parametric Method to Resolve the Ill-Posed Nature of the EIT Reconstruction Problem: A Simulation Study

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The reconstruction problem of electrical impedance tomography (EIT) is to estimate the distribution of the conductivity inside an object from measured potential distributions on the circumference caused by injected current patterns. Mathematically, this reconstruction problem is an ill-posed nonlinear inverse problem, with many unknowns. In this paper, the ill-posed nature is demonstrated by analyzing the condition of the sensitivity matrix; the associated inverse problem can only be solved on a very coarse grid. To circumvent the ill-posed nature of the EIT reconstruction problem, we present a new parametric formulation. In this formulation, it is assumed that the object consists of compartments with homogeneous conductivity. The position, orientation, size, and conductivity of these compartments are treated as unknown parameters, which are determined by solving the forward problem (using the boundary element method) and optimizing the parameters (using Powell's or the simplex method) in order to fit the parameters to the EIT data. Simulations show that the parametric method is stable and adequately solves the EIT problem.

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