From Multiresolution to the System-by-Design based GPR Imaging
Authors: Zardi Francesco , Poli Lorenzo , Massa Andrea 
Published: March 2022

&lt;p&gt;Ground Penetrating Radar (&lt;em&gt;GPR&lt;/em&gt;) 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 (&lt;em&gt;EM&lt;/em&gt;) characteristics of the imaged objects. Such a task can be formulated as an Inverse Scattering Problem (&lt;em&gt;ISP&lt;/em&gt;), whose solution poses paramount challenges due to the ill-posedness and non-linearity [1]. Therefore, &quot;smart&quot; 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 &lt;em&gt;GPR&lt;/em&gt; imaging methodologies is an active research area of the ELEDIA Research Center at the University of Trento, Italy. &lt;em&gt;GPR&lt;/em&gt; microwave imaging strategies based on the Multiresolution (&lt;em&gt;MR&lt;/em&gt;) paradigm demonstrated significant improvements in terms of reconstruction accuracy and inversion time [2]-[5]. The strength of the &lt;em&gt;MR&lt;/em&gt; framework stems from balancing the number of unknowns with the amount of available data, reducing the non-linearity of the &lt;em&gt;ISP&lt;/em&gt;. Moreover, it allows a straightforward exploitation of the &quot;progressively-acquired&quot; information on the imaged domain, resulting in a mitigation of the ill-posedness. Effective &lt;em&gt;MR&lt;/em&gt; strategies have been recently proposed based on the exploitation of stochastic optimization algorithms [4] to mitigate the risk of false solutions. Recently, an &lt;em&gt;MR&lt;/em&gt;-based solution strategy has been proposed that exploits an Inexact Newton method developed in L&lt;sup&gt;p&lt;/sup&gt; spaces to achieve better regularization of the subsurface &lt;em&gt;ISP&lt;/em&gt; thanks to the joint processing of multiple spectral components of &lt;em&gt;GPR&lt;/em&gt; data [5]. Another solution paradigm significantly improving the performance of &lt;em&gt;GPR&lt;/em&gt; data inversion is the System-by-Design (&lt;em&gt;SbD&lt;/em&gt;) [6][7]. The &lt;em&gt;SbD&lt;/em&gt;, defined as &quot;&lt;em&gt;a framework to deal with complexity&lt;/em&gt;&quot; in &lt;em&gt;EM&lt;/em&gt; problems [6] leverages on the recent advancements in the area of Learning-by-Examples techniques and it allows a proper reformulation of the &lt;em&gt;ISP&lt;/em&gt; enabling the &quot;smart&quot; 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].&amp;#160;&lt;/p&gt;&lt;p&gt;&lt;em&gt;References&lt;/em&gt;&lt;/p&gt;&lt;p&gt;[1] R. Persico, &lt;em&gt;Introduction to Ground Penetrating Radar: Inverse Scattering and Data Processing&lt;/em&gt;. Hoboken, New Jersey: Wiley, 2014.&lt;br&gt;[2] M. Salucci et al. &amp;#8220;GPR prospecting through an inverse-scattering frequency-hopping multifocusing approach,&amp;#8221; &lt;em&gt;IEEE Trans. Geosci. Remote Sens.&lt;/em&gt;, vol. 53, no. 12, pp. 6573-6592, Dec. 2015.&lt;br&gt;[3] M. Salucci et al., &amp;#8220;Advanced multi-frequency GPR data processing for non-linear deterministic imaging,&amp;#8221; &lt;em&gt;Signal Process.&lt;/em&gt;, vol. 132, pp. 306&amp;#8211;318, Mar. 2017.&lt;br&gt;[4] M. Salucci et &lt;em&gt;al.&lt;/em&gt;, &amp;#8220;Multifrequency particle swarm optimization for enhanced multiresolution GPR microwave imaging,&amp;#8221; &lt;em&gt;IEEE Trans. Geosci. Remote Sens.&lt;/em&gt;, vol. 55, no. 3, pp. 1305-1317, Mar. 2017.&lt;br&gt;[5] M. Salucci et &lt;em&gt;al.&lt;/em&gt;, &amp;#8220;2-D TM GPR imaging through a multiscaling multifrequency approach in Lp spaces,&amp;#8221; &lt;em&gt;IEEE Trans. Geosci. Remote Sens.&lt;/em&gt;, vol. 59, no. 12, pp. 10011-10021, Dec. 2021.&lt;br&gt;[6] A. Massa and M. Salucci, &amp;#8220;On the design of complex EM devices and systems through the System-by-Design paradigm - A framework for dealing with the computational complexity,&amp;#8221; &lt;em&gt;IEEE Trans. Antennas Propag.&lt;/em&gt;, &lt;em&gt;in press&lt;/em&gt; (DOI: 10.1109/TAP.2021.3111417).&lt;br&gt;[7] M. Salucci et &lt;em&gt;al.&lt;/em&gt;, &quot;Learned global optimization for inverse scattering problems - Matching global search with computational efficiency,&quot; &lt;em&gt;IEEE Trans. Antennas Propag.&lt;/em&gt;, &lt;em&gt;in press &lt;/em&gt;(DOI: 10.1109/TAP.2021.3139627).&lt;/p&gt;