From Multiresolution to the System-by-Design based GPR Imaging

Ground Penetrating Radar (GPR) is a technology of high interest due to its many applications [1], requiring to process the collected data to retrieve the shape and/or electromagnetic (EM) characteristics of the imaged objects. Such a task can be formulated as an Inverse Scattering Problem (ISP), whose solution poses paramount challenges due to the ill-posedness and non-linearity [1]. Therefore, "smart" solution approaches must be developed capable of fully exploiting the available/acquired information to achieve satisfying reconstructions with limited computational resources. In this framework, the development of innovative GPR imaging methodologies is an active research area of the ELEDIA Research Center at the University of Trento, Italy. GPR microwave imaging strategies based on the Multiresolution (MR) paradigm demonstrated significant improvements in terms of reconstruction accuracy and inversion time [2]-[5]. The strength of the MR framework stems from balancing the number of unknowns with the amount of available data, reducing the non-linearity of the ISP. Moreover, it allows a straightforward exploitation of the "progressively-acquired" information on the imaged domain, resulting in a mitigation of the ill-posedness. Effective MR strategies have been recently proposed based on the exploitation of stochastic optimization algorithms [4] to mitigate the risk of false solutions. Recently, an MR-based solution strategy has been proposed that exploits an Inexact Newton method developed in L^p spaces to achieve better regularization of the subsurface ISP thanks to the joint processing of multiple spectral components of GPR data [5]. Another solution paradigm significantly improving the performance of GPR data inversion is the System-by-Design (SbD) [6][7]. The SbD, defined as "a framework to deal with complexity" in EM problems [6] leverages on the recent advancements in the area of Learning-by-Examples techniques and it allows a proper reformulation of the ISP enabling the "smart" reduction of its unknowns and the definition of a fast surrogate model to markedly reduce the computational burden of multi-agent evolutionary-inspired optimization tools [6][7]. 

References

[1] R. Persico, Introduction to Ground Penetrating Radar: Inverse Scattering and Data Processing. Hoboken, New Jersey: Wiley, 2014.
[2] M. Salucci et al. “GPR prospecting through an inverse-scattering frequency-hopping multifocusing approach,” IEEE Trans. Geosci. Remote Sens., vol. 53, no. 12, pp. 6573-6592, Dec. 2015.
[3] M. Salucci et al., “Advanced multi-frequency GPR data processing for non-linear deterministic imaging,” Signal Process., vol. 132, pp. 306–318, Mar. 2017.
[4] M. Salucci et al., “Multifrequency particle swarm optimization for enhanced multiresolution GPR microwave imaging,” IEEE Trans. Geosci. Remote Sens., vol. 55, no. 3, pp. 1305-1317, Mar. 2017.
[5] M. Salucci et al., “2-D TM GPR imaging through a multiscaling multifrequency approach in Lp spaces,” IEEE Trans. Geosci. Remote Sens., vol. 59, no. 12, pp. 10011-10021, Dec. 2021.
[6] A. Massa and M. Salucci, “On the design of complex EM devices and systems through the System-by-Design paradigm - A framework for dealing with the computational complexity,” IEEE Trans. Antennas Propag., in press (DOI: 10.1109/TAP.2021.3111417).
[7] M. Salucci et al., "Learned global optimization for inverse scattering problems - Matching global search with computational efficiency," IEEE Trans. Antennas Propag., in press (DOI: 10.1109/TAP.2021.3139627).