Selecting a Mesh for Chemical Species Tomography with Bayesian Model Comparison

Abstract:
Gas distributions reconstructed by chemical species tomography (CST) vary in quality due to the discretization scheme, arrangement of optical paths, errors in the measurement model, and prior information used to close the inversion. There is currently a lack of mathematically-rigorous frameworks for comparing the finite bases available to discretize a CST domain. Following the Bayesian formulation of tomography, we show that Bayesian model selection can identify the mesh density, mode of interpolation, and prior information best-suited to reconstruct a set of measurements. We validate this procedure with a simulated CST experiment, and generate accurate reconstructions despite limited measurement information. Moreover, we apply the finite element method to represent the flow field. We use Bayesian model selection to choose between three forms of polynomial support for a range of mesh resolutions, as well as four priors. This work demonstrates that the model likelihood of Bayesian model selection is a good predictor of reconstruction accuracy.

Biography:
Samuel Grauer is a Ph.D. candidate at the University of Waterloo where he researches statistical imaging techniques that are used to study gas jets and flames. He is currently a member of NSERC’s FlareNet research network, working on a gas detection algorithm using hyperspectral data. And in 2017 he was resident at the University of Duisburg-Essen, as a visiting scholar, where he developed a 3D flame tomography system based on background-oriented schlieren imaging. Samuel received a B.Sc. in mechanical engineering from the University of Manitoba in 2014.