This paper discusses a novel technique of estimating gas temperatures
based on impedance tomography. More specifically, assume that we have
a gas funnel (e.g. doorway, window, chimney) equipped with a mesh of t
hin electrically conducting filaments. Furthermore, assume that the th
ermal and thermoelectric properties of the conducting material are kno
wn. The temperature mapping method is based on changes of the resistiv
ity of the filaments by the changes in temperature. The inverse proble
m is closely related to the standard tomography problem. Due to the se
vere underdetermination of the problem, common inversion techniques us
ed in computerized tomography cannot be employed here. The problem is,
therefore, recast in a form of a Bayesian parameter estimation proble
m. Markov chain Monte Carlo methods (MCMC) are applied for exploring t
he posterior distribution.