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The inspection of underground scenarios is a challenging task required in several applications, from geophysical to archeological and civil areas. The ground penetrating radar (GPR) is a common tool that has been widely adopted to provide qualitative imaging of the underground scenario [1]. Recently, several approaches to process GPR data and retrieve quantitative images to characterize the inspected region have been developed [2-3]. Moreover, to compensate for the loss of information that usually happens in this scenario, GPR systems have been implemented not only in monostatic and bistatic configurations but also in multistatic settings [4].In this contribution, a quantitative inverse scattering approach is proposed to retrieve the distribution of the complex dielectric permittivity of a buried region, starting from scattering parameters collected through a multistatic GPR configuration. The approach is based on a finite-element (FE) formulation of the electromagnetic inverse scattering problem and, as solving procedure, a reconstruction method in variable exponent Lebesgue spaces is adopted [5]. On the one hand, the FE model embedded in the method is exploited to describe the structure of the measurement configuration without simplifying assumptions (except for the two-dimensional hypotheses and the numerical discretization of the problem). On the other hand, the inversion procedure in variable exponent Lebesgue spaces has been found quite effective to face the ill-posedness and nonlinearity of the problem. A numerical validation of this approach is reported. References[1] R. Persico, “Introduction to ground penetrating radar: Inverse scattering and data processing.” Hoboken, New Jersey: Wiley, 2014.[2] M. Pastorino and A. Randazzo, “Microwave imaging methods and applications.” Boston, MA: Artech House, 2018.[3] V. Schenone, A. Fedeli, C. Estatico, M. Pastorino, and A. Randazzo, “Experimental assessment of a novel hybrid scheme for quantitative GPR imaging”, IEEE Geoscience and Remote Sensing Letters, vol. 19, pp. 1–5, 2022.[4] M. Ambrosanio, M. T. Bevacqua, T. Isernia, and V. Pascazio, “Performance analysis of tomographic methods against experimental contactless multistatic ground penetrating radar”, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 14, pp. 1171–1183, 2021.[5] V. Schenone, C. Estatico, G. L. Gragnani, M. Pastorino, A. Randazzo, and A. Fedeli, “Microwave-based subsurface characterization through a combined finite element and variable exponent spaces technique”, Sensors, vol. 23, no. 1, p. 167, 2023. |
