Speed improvement of MCMC image reconstruction in tomography by partial linearization

Robert M. West, Manuchehr Soleimani, Robert G. Aykroyd, & William RB Lionheart

Electrical impedance tomography is cast in the framework of Bayesian modelling, providing a natural setting in which to specify and interpret regularization. Solution is based on Markov chain Monte Carlo simulated samples from the posterior distribution. To be computationally viable, many solutions of the direct solutions must be calculated. This is achieved by partial linearization of the direct solution. Full solutions are still undertaken once in 50 steps in the chain. With the efficiency gain, a factor of 40, Markov chain Monte Carlo image reconstruction becomes an attractive technique for electrical impedance tomography. Benefits include the specification of standard deviations for the reconstructed image and a range of credible solutions can be assessed rather than a single best solution.

Keywords: 3D EIT, Inverse Problems, MCMC, Linearization