We examine sample based Bayesian inference from impedance imaging data. We report experiments employing low level pixel based priors with mixed discrete and continuous conductivities. Sampling is carried out using Metropolis- Hasting Markov chain Monte Carlo, employing both large scale, Langevin updates, and state-adaptive local updates. Computing likelihood ratios of conductivity distributions involves solving a second order linear partial differential equation. However our simulation is rendered computationally tractable by an update procedure which employs a linearization of the forward map and thereby avoids solving the PDE for those updates which are rejected.
Geoff K. Nicholls,
"Prior modeling and posterior sampling in impedance imaging", Proc. SPIE 3459, Bayesian Inference for Inverse Problems, (22 September 1998); doi: 10.1117/12.323791; https://doi.org/10.1117/12.323791