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

<p>Ground Penetrating Radar (<em>GPR</em>) 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>EM</em>) characteristics of the imaged objects. Such a task can be formulated as an Inverse Scattering Problem (<em>ISP</em>), 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 <em>GPR</em> imaging methodologies is an active research area of the ELEDIA Research Center at the University of Trento, Italy. <em>GPR</em> microwave imaging strategies based on the Multiresolution (<em>MR</em>) paradigm demonstrated significant improvements in terms of reconstruction accuracy and inversion time [2]-[5]. The strength of the <em>MR</em> framework stems from balancing the number of unknowns with the amount of available data, reducing the non-linearity of the <em>ISP</em>. Moreover, it allows a straightforward exploitation of the "progressively-acquired" information on the imaged domain, resulting in a mitigation of the ill-posedness. Effective <em>MR</em> strategies have been recently proposed based on the exploitation of stochastic optimization algorithms [4] to mitigate the risk of false solutions. Recently, an <em>MR</em>-based solution strategy has been proposed that exploits an Inexact Newton method developed in L<sup>p</sup> spaces to achieve better regularization of the subsurface <em>ISP</em> thanks to the joint processing of multiple spectral components of <em>GPR</em> data [5]. Another solution paradigm significantly improving the performance of <em>GPR</em> data inversion is the System-by-Design (<em>SbD</em>) [6][7]. The <em>SbD</em>, defined as "<em>a framework to deal with complexity</em>" in <em>EM</em> problems [6] leverages on the recent advancements in the area of Learning-by-Examples techniques and it allows a proper reformulation of the <em>ISP</em> 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]. </p><p><em>References</em></p><p>[1] R. Persico, <em>Introduction to Ground Penetrating Radar: Inverse Scattering and Data Processing</em>. Hoboken, New Jersey: Wiley, 2014.<br>[2] M. Salucci et al. “GPR prospecting through an inverse-scattering frequency-hopping multifocusing approach,” <em>IEEE Trans. Geosci. Remote Sens.</em>, vol. 53, no. 12, pp. 6573-6592, Dec. 2015.<br>[3] M. Salucci et al., “Advanced multi-frequency GPR data processing for non-linear deterministic imaging,” <em>Signal Process.</em>, vol. 132, pp. 306–318, Mar. 2017.<br>[4] M. Salucci et <em>al.</em>, “Multifrequency particle swarm optimization for enhanced multiresolution GPR microwave imaging,” <em>IEEE Trans. Geosci. Remote Sens.</em>, vol. 55, no. 3, pp. 1305-1317, Mar. 2017.<br>[5] M. Salucci et <em>al.</em>, “2-D TM GPR imaging through a multiscaling multifrequency approach in Lp spaces,” <em>IEEE Trans. Geosci. Remote Sens.</em>, vol. 59, no. 12, pp. 10011-10021, Dec. 2021.<br>[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,” <em>IEEE Trans. Antennas Propag.</em>, <em>in press</em> (DOI: 10.1109/TAP.2021.3111417).<br>[7] M. Salucci et <em>al.</em>, "Learned global optimization for inverse scattering problems - Matching global search with computational efficiency," <em>IEEE Trans. Antennas Propag.</em>, <em>in press </em>(DOI: 10.1109/TAP.2021.3139627).</p>