A stochastic simulation method for uncertainty quantification in the linearized inverse conductivity problem

This paper considers the inverse problem in electrical impedance tomography with non-informative prior information on the required conductivity function. The problem is approached with a Newton-type iterative algorithm where the solution of the linearized approximation is estimated using Bayesian inference. The novelty of this work focuses on maximum a posteriori estimation assuming a model that incorporates the linearization error as a random variable. From an analytical expression of this term, we employ Monte Carlo simulation in order to characterize its probability distribution function. This simulation entails sampling an improper prior distribution for which we propose a stable scheme on the basis of QR decomposition. The simulation statistics show that the error on the linearized model is not Gaussian, however, to maintain computational tractability, we derive the posterior probability density function of the solution by imposing a Gaussian kernel approximation to the error density. Numerical results obtained through this approach indicate the superiority of the new model and its respective maximum a posteriori estimator against the conventional one that neglects the impact of the linearization error. Copyright (C) 2011 John Wiley & Sons, Ltd.