Application of Bayesian neural network in electrical impedance tomography

In this contribution we present a method for solving the inverse problem in electric impedance tomography with neural networks. The problem of reconstructing the conductivity distribution inside an object from potential measurements on the surface is known to be ill-posed requiring efficient regularization techniques. We demonstrate that a statistical inverse solution, where the mean of the inverse mapping is approximated with a neural network gives promising results. We study the effect of input and output data representation by simulations and conclude that projection to principal axis is feasible data transformation. Also we demonstrate that Bayesian neural networks, which aim to average over all network models weighted by the model´s posterior probability provide the best reconstruction results. With the presented approach estimation of some target variables, such as the void fraction (the ratio of gas and liquid), may be applicable directly without the actual image reconstruction. We also demonstrate that the solutions are very robust against noise in inputs