Electromagnetic inversion systems require that the experimental data be calibrated to the computational inversion model being used. In addition, accurate prior information provided to the inversion algorithm leads to higher-quality images. For some applications of inversion, such as stored grain imaging or geophysical inversion, known (calibration) targets cannot be easily introduced into the imaging region and the ability to determine prior information can be limited. In an attempt to solve the problem of calibrating data from such field-inversion systems, we introduce a work flow where: (1) a simple parametric physical model of the scattering background is obtained via a phaseless (magnitude only data) inversion algorithm that works on phase-corrupted, uncalibrated total-field measurements, and (2) we then use this simple physical model to generate calibration and prior information for subsequent full-data (magnitude and phase) inversion. Using an example of in-bin stored grain imaging, the inverted parameters are the grain angle of repose, grain height, and the average bulk permittivity of the grain. Using uncalibrated total-field data, we show that the proposed work flow obtains the overall structure of the grain in a bin despite the use of this raw data. We then show that the simple physical model can be used as both a calibration data set as well as the prior information about the grain target in a full-data (magnitude and phase) inversion. The use of this phaseless algorithm means we are able to remotely calibrate imaging systems, and obtain critical prior information about the imaging region without introducing a calibration target or physically measuring the imaging region in other ways.INDEX TERMS Inverse problems, calibration, microwave tomography, inverse imaging.

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We present a neural network architecture to determine the volume and complex permittivity of grain stored in metal bins. The neural networks output the grain height, cone angle and complex permittivity of the grain, using the input of experimental field data (S-parameters) from an electromagnetic imaging system consisting of 24 transceivers installed in the bin. Key for practical applications, the neural networks are trained on synthetic data sets but generate the parametric information using experimental data as input, without the use of calibration objects or open-short-load measurements. To accomplish this, we formulate a data normalization scheme that enables the use of a loss function that directly compares measured S-parameters and simulation model fields. The normalization strategy and the ability to train on synthetic data means we do not need to collect experimental training data. We demonstrate the applicability of this synthetically trained neural network to experimental data from two different bin geometries, and discuss the ability of these neural networks to successfully infer parameters that can be used for grain inventory management. Our neural-network-based approach enables rapid inference, providing a more cost-effective long-term solution than existing optimization-based parametric inversion methods.

Abstract-Novel microwave imaging systems require flexible forward solvers capable of incorporating arbitrary boundary conditions and inhomogeneous background constitutive parameters. In this work we focus on the implementation of a time-harmonic Discontinuous Galerkin Method (DGM) forward solver with a number of features that aim to benefit tomographic microwave imaging algorithms: locally varying high-order polynomial field expansions, locally varying high-order representations of the complex constitutive parameters, and exact radiating boundary conditions. The DGM formulated directly from Maxwell's curl equations facilitates including both electric and magnetic contrast functions, the latter being important when considering quantitative imaging with magnetic contrast agents. To improve forward solver performance we formulate the DGM for time-harmonic electric and magnetic vector wave equations driven by both electric and magnetic sources. Sufficient implementation details are provided to permit existing DGM codes based on nodal expansions of Maxwell's curl equations to be converted to the wave equation formulations. Results are shown to validate the DGM forward solver framework for transverse magnetic problems that might typically be found in tomographic imaging systems, illustrating how high-order expansions of the constitutive parameters can be used to improve forward solver performance.