Abstract
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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> 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.
Highlights
M ICROWAVE tomography (MWT) use-cases in the industry are mostly for monitoring and inspection purposes, as reported in [1]–[3]
To generate the numerical measurement data from the MWT setup shown in Fig. 1 a finite element method (FEM) based COMSOL simulation tool is chosen
They are compared separately for the real and imaginary parts for the two prior models. It is clear from resemblance coefficient (RC) and root mean square error (RMSE) values that the overall accuracy of the maximum a posteriori estimates (MAP) estimate has improved with the sample-based prior model in both the cases
Summary
M ICROWAVE tomography (MWT) use-cases in the industry are mostly for monitoring and inspection purposes, as reported in [1]–[3]. One of the solutions to eliminate the problem of thermal runaway and hot-spot formation is intelligent control of power sources (magnetrons) to obtain a selective heating rate at each stage of the drying process [7], [8] To apply such a precise microwave power control in-situ and noninvasive measurement of the unknown distribution of moisture inside the porous material is required. For estimating the moisture levels (in terms of dielectric constant) in a porous material with a large cross-sectional dimension, we apply a statistical inversion approach [12] based on the Bayesian framework. The performance of the proposed correlated sample based prior model is first evaluated with numerical scattered field data from the 2-D MWT setup for three moisture scenarios.
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