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

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 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 crosssection of a 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.

Multistatic Uniform Diffraction Tomography Derived Structural-Prior in Bayesian Inversion Framework for Microwave Tomography

“…It is often ignored since it requires integration over all possible ϵ r . The likelihood density, if the noise is assumed to be additive Gaussian with zero mean with the covariance matrix Γ ξ , can be written as [31] π…”

“…Note here that the standard deviations terms control the amplitude of real and imaginary parts of dielectric constant in the prior covariance matrix. These values can be determined using the dielectric characterisation of the foam which is described in details in [31], [37]. The moisture field variation in terms of real part of dielectric constant can be expressed as [38]…”

A Review on Fast Tomographic Imaging Techniques and Their Potential Application in Industrial Process Control

“…This might be because most of the current measurement devices and reconstruction algorithms, especially when multi-frequency data and non-linear reconstruction algorithms are used, do not reach the sub-second speed requirements of the control systems. Therefore, to meet the speed requirement of the control, strategies such as limited-band or single-frequency reconstructions, utilizing, for example, machine learning or linearized inversion schemes, can be adopted, in combination with a custom-built data acquisition setup [ 88 , 89 , 90 ]. In addition, MWT has several important features, such as safety due to the low-level operating power, good contrast, and completely contactless operation, which make it a potential choice for control applications in various industrial processes.…”