Gibbs samplers have many desirable theoretical properties, but also have the pesky requirement that conditional distributions be available. We show how conditional densities can be evaluated for the posterior distribution in conductivity imaging - virtually for free in coordinate directions and very cheaply in other ‘special’ directions. The analysis actually applies to a broad class of non-invasive imaging techniques that utilize strong scattering of energy, and leads to efficient iterative algorithms whether implementing inference or optimization. The resulting Gibbs sampler draws an independent conductivity image in only a little more compute time than required for optimization.
Colin Fox, Colin Fox,
"A Gibbs sampler for conductivity imaging and other inverse problems", Proc. SPIE 8500, Image Reconstruction from Incomplete Data VII, 850006 (15 October 2012); doi: 10.1117/12.931111; https://doi.org/10.1117/12.931111