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.

Keywords

• Inverse problems
• calibration
• microwave tomography
• inverse imaging