A FEM-based nonlinear MAP estimator in electrical impedance tomography
Electrical impedance tomography of closed conductive media is an ill-posed inverse problem. Using the finite elements method to solve the corresponding direct problem allows one to preserve the nonlinear dependence of the observation set upon the conductivity distribution. We show that the Bayesian approach presented by Demoment (1989) for linear inverse imaging problems is still valid for such a nonlinear inverse problem. Our contribution is based on an edge-preserving Markov model as a prior for conductivity distribution. Maximum a posteriori reconstruction results from 40-dB noisy measurements (simulated with a finer mesh) yield significant resolution improvement compared to classical methods.