Phaseless Parametric Inversion for System Calibration and Obtaining Prior Information

Abstract

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.

Imaging and Calibration of Electromagnetic Inversion Data With a Single Data Set

“…Grain-bin EMI allows the reconstruction of 3D maps of the permittivity inside the bin which can be used to monitor the grain for safe storage conditions over time. Results for such systems have been previously reported in [2], [3], [4], [5].…”

A Machine Learning Workflow for Tumour Detection in Breasts Using 3D Microwave Imaging

“…Imaging multi-wavelength high-contrast targets, such as the human breast in air, is extremely difficult without the use of accurate background information to reduce the contrast in the non-linear imaging problem [4,16]. However, seeking bulk parameters using standard optimization techniques is computationally expensive [33]. As a result of these two facts, we propose a workflow for microwave breast imaging that consists of two distinct stages: Stage 1, bulk parameter (prior information) inference, and Stage 2, image reconstruction.…”

“…We have recently had success extracting bulk imaging parameters from phaseless electromagnetic field data in the application which are stored grain monitoring. In grain bin imaging, the parameters consisting of grain height, angle of repose and bulk complexvalued permittivity, are obtained using either an iterative optimization technique [33] or machine learning using either single-frequency data [34] or multi-frequency data [35]. The machine learning approach provides a cost-effective, near real-time, long-term monitoring solution where the cost of a computationally expensive optimization for every measurement is instead transferred to one-time network training.…”

“…The machine learning approach provides a cost-effective, near real-time, long-term monitoring solution where the cost of a computationally expensive optimization for every measurement is instead transferred to one-time network training. We have demonstrated both synthetically and experimentally that these parameters can be used for calibration and as prior information for full phase 3-D inversion of grain stored in a large metal grain bin [33].…”

“…No experimental data is required for training the machine learning model presented in this work. An additional contribution includes the generalization of the machine-learning work-flow originally developed for grain-bin imaging to microwave breast imaging [33][34][35].…”