Correlated Sample-Based Prior in Bayesian Inversion Framework for Microwave Tomography

When using the statistical inversion framework in microwave tomography (MWT), generally, the real and imaginary parts of the unknown dielectric constant are treated as uncorrelated and independent random variables. Thereby, in the maximum a posteriori estimates, the two recovered variables may show different structural changes inside the imaging domain. In this work, a correlated sample-based prior model is presented to incorporate the correlation of the real part with the imaginary part of the dielectric constant in the statistical inversion framework. The method is used to estimate the inhomogeneous moisture distribution (as dielectric constant) in a large cross section of polymer foam. The targeted application of MWT is in industrial drying to derive intelligent control methods based on tomographic inputs for selective heating purposes. One of the features of the proposed method shows how to integrate lab-based dielectric characterization, often available in MWT application cases, in the prior modeling. The method is validated with numerical and experimental MWT data for the considered moisture distributions.