This work considers the inclusion detection problem of electrical impedance tomography with stochastic conductivities. It is shown that a conductivity anomaly with a random conductivity can be identified by applying the factorization method or the monotonicity method to the mean value of the corresponding Neumann-to-Dirichlet map provided that the anomaly has high enough contrast in the sense of expectation. The theoretical results are complemented by numerical examples in two spatial dimensions.
Barth, A., Harrach, B., Hyvönen, N., & Mustonen, L. (2017). Detecting stochastic inclusions in electrical impedance tomography. Inverse Problems, 33(11), 1-18. . https://doi.org/10.1088/1361-6420/aa8f5c