Imaging convex quadrilateral inclusions in uniform conductors from electrical boundary measurements

We demonstrate simulation-based Bayesian imaging from electrical impedance tomographic data, by summarizing the set of conductance images which could give rise to the data. The forward map from conductance image to data requires the solution of a partial differential equation subject to boundary conditions. We develop the example of recovering an unknown convex polygonal insulating inclusion within an object made of otherwise uniformly conducting material, and illustrate our methods with noisy synthetic data. Sampling is carried out using Markov chain Monte Carlo with the efficiency of the algorithm investigated over a range of noise levels.