Bayes-MCMC Reconstruction from 3D EIT Data Using a Combined Linear and Non-Linear Forward Problem Solution Strategy

Extracting meaningful information from EIT data is a challenging task due to highly correlated data and substantial noise. Domain discretisation further complicates the situation by also making it an ill-posed problem requiring substantial regularisation. The Bayesian approach not only provides a natural setting in which to specify and interpret regularisation, but also leads to distributional results allowing probabilistic statements to be made, such as confidence intervals. When combined with MCMC methods great flexibility in modelling and output summary is possible. A major issue, however, when using MCMC algorithms is the number of times the forward problem must be solved. In many cases this means that the computational time is prohibitive this is particularly true for 3D problems. This paper proposes the mixing of full non-linear solution of the forward problem with linearised solution. The linear approximation works well for local changes in the solution and so is ideally suited to use in MCMC algorithms. Over multiple iterations, however, repeated linearisation accumulates errors and so strategic full nonlinear solutions are used to correct the path of the algorithm. The combined strategy provides a reliable approach with computational times that make the MCMC method feasible in practical situations.