Estimation of contour parameter uncertainties in permittivity imaging using MCMC sampling

Electrical capacitance tomography is targeted on estimating the spatial permittivity distribution of an inhomogeneous medium from measurements of trans-capacitance of a multi-electrode assembly outside the boundary of the medium. Since small changes in the measured data cause large or unbounded changes in recovered parameters, the problem is an ill-posed inverse problem. In this article, special focus is on the robust reconstruction of the shape of material inhomogeneities in an otherwise uniform background material. In order to represent the boundary of the inclusion, radial basis functions (RBF) implying a low order of the state-space are introduced. This approach ensures smooth contours how they appear in industrial applications like in oil refinement. The inverse problem is formulated in a Bayesian inferential framework, by specifying a prior distribution for the shape of the inclusion, and characterizing the statistics of measurement noise. The Markov chain Monte Carlo (MCMC) is presented to efficiently explore the posterior distribution. The applicability of the proposed MCMC sampler is verified for a reconstruction example using measured data.