Abstract
Electrical impedance tomography (EIT) is a well-known technique to estimate the conductivity distribution γ of a body Ω with unknown electromagnetic properties. EIT is a severely ill-posed inverse problem. In this paper, we formulate the EIT problem in the Bayesian framework using mixed total variation (TV) and non-convex ℓp regularization prior. We use the Markov Chain Monte Carlo (MCMC) method for sampling the posterior distribution to solve the ill-posed inverse problem in EIT. We present simulations to estimate the distribution for each pixel for the image reconstruction of the conductivity in EIT.
Funding source: US National Science Foundation
Award Identifier / Grant number: DMS 0915214
The authors would like to acknowledge the reviewers for their valuable comments and input in improving the manuscript. In particular, we thank the reviewers for their helpful editorial comments in making the manuscript more readable for a broader audience. The second author would like to acknowledge the support from the Alexander von Humboldt Foundation for research that motivated the analytical approach summarized in this paper which appeared in previous work in collaboration with Professor Peter Maass (University of Bremen, Germany) and Dr. Bangti Jin (Texas A&M University, USA). The second author also acknowledges the support of the US National Science Foundation grant (DMS 0915214) that motivated this work.
© 2015 by De Gruyter
