Quantitative Inversion of Multiantenna Ground-Penetrating Radar Data with Modeling Error Correction Based on Long Short-Term Memory Cells

Abstract

Quantitative inversion of GPR data opens the door to precise characterization of underground environments. However, in order to make the inverse scattering problem solution easier from a computational viewpoint, simplifying assumptions are often applied, i.e., two-dimensional approximations or the consideration of idealized field probes and electromagnetic sources. These assumptions usually produce modeling errors, which can degrade the dielectric reconstruction results considerably. In this article, a processing step based on long short-term memory cells is proposed for the first time to correct the modeling error in a multiantenna GPR setting. In particular, time-domain GPR data are fed into a neural network trained with couples of finite-difference time-domain simulations, where a set of sample targets are simulated in both realistic and idealized configurations. Once trained, the neural network outputs an approximation of multiantenna GPR data as they are collected by an ideal two-dimensional measurement setup. The inversion of the processed data is then accomplished by means of a regularizing Newton-based nonlinear scheme with variable exponent Lebesgue space formulation. A numerical study has been conducted to assess the capabilities of the proposed inversion methodology. The results indicate the possibility of effectively compensating for modeling error in the considered test cases.