Chrysoula Tsogka

Motivated by the use of unmanned aerial vehicles (UAVs) equipped with ground penetrating synthetic aperture radar (GP-SAR) for imaging buried landmines, we study imaging of subsurface targets. A key challenge in this problem is the removal of so-called ground bounce signals which are reflections from the air-soil interface. When ground bounce signals can be removed exactly from GP-SAR measurements, one can readily image subsurface targets using traditional synthetic aperture imaging methods such as Kirchhoff migration (KM). However, ground bounce signals dominate measurements, carry no useful information about subsurface targets, and disrupt their imaging. In this paper we present an asymptotic theory for this problem assuming that the elevation of the UAV flight path is the largest length scale in the problem. Using this asymptotic theory, we introduce data-driven methods for (i) estimating the ground permittivity, and (ii) approximately removing ground bounce signals from GP-SAR. We first establish these methods for the simple case of a flat air-soil interface and then apply them to an unknown rough air-soil interface. We validate this asymptotic theory using numerical simulations.

Wave propagation in multilayered media with high material contrasts poses significant numerical challenges, as large variations in wavenumbers lead to strong reflections and complex transmission of the incoming wave field. To address these difficulties, we employ a boundary integral formulation thereby avoiding volumetric discretization. In this framework, the accuracy of the numerical solution depends strongly on how the material interfaces are discretized. In this work, we demonstrate that standard meshing strategies based on resolving the maximum wavenumber across the domain become computationally inefficient in multilayered configurations, where high wavenumbers are confined to localized subdomains. Through a systematic study of multilayer transmission problems, we show that no simple discretization rule based on the maximum wavenumber or material contrasts emerges. Instead, the wavenumber of the background (exterior) medium plays a dominant role in determining the optimal boundary resolution. Building on these insights, we propose an adaptive approach that achieves uniform accuracy and efficient computation across multiple layers. Numerical experiments for a range of multilayer configurations demonstrate the scalability and robustness of the proposed approach.

We propose a methodology that exploits large and diverse datasets to accurately estimate the ambient medium’s Green’s functions in strongly scattering media. Given these estimates, excellent imaging results are achieved, with a resolution that is better than that of a homogeneous medium. This phenomenon, known as superresolution, arises because the ambient scattering medium effectively enlarges the physical imaging aperture. While superresolution has been demonstrated and analyzed extensively in the context of physical time reversal, time reversal itself is not imaging. Our proposed methodology, based on either conventional optimization methods or neural networks, makes it possible to achieve superresolution imaging in complex media.

When target sizes are comparable to the inherent resolution of a synthetic aperture radar (SAR) imaging system, images only produce representative points which can be used to detect and locate different targets, but not distinguish any further between them. Using those representative points reconstructed with traditional SAR imaging, we introduce a method that recovers a frequency spectrum from the same set of measurements. We show theoretically that this spectrum is related to the radar cross‐section of the target. For special cases when the proposed method is not able to distinctly image or recover frequency spectra from two different targets, we introduce modifications that resolve those issues. Using numerical simulations, we show that this spectrum provides valuable information allowing for differentiating targets that would otherwise be indistinguishable. Moreover, this method does not require any additional data than that already used for imaging. Including this spectral characterization opens opportunities to consider alternate strategies for managing resources for collecting and recovering target features contained in SAR measurements.

When target sizes are comparable to the inherent resolution of a synthetic aperture radar (SAR) imaging system, images only produce representative points which can be used to detect and locate different targets but not distinguish any further between them. Using those representative points from the reconstructed image, we introduce a method that recovers a frequency spectrum from the same set of measurements. We show theoretically that this spectrum is related to the radar cross-section (RCS) of the target. For special cases when the proposed method is not able to distinctly image or recover frequency spectra from two different targets, we introduce modifications that resolve those issues. Using numerical simulations, we show that this spectrum provides valuable information allowing for differentiating targets that would otherwise be indistinguishable. Moreover, this method does not require any additional data than that already used for imaging. Including this spectral characterization opens opportunities to consider alternate strategies for managing resources for collecting and recovering target features contained in SAR measurements.

We study ground-penetrating synthetic aperture radar measurements of scattering by targets located below a rough air-soil interface. By considering the inherent space/angle limitations of this imaging modality, we introduce a simplified model for measurements. This model assumes (i) first-order interactions between the target and the air-soil interface, (ii) scattering by the target below a flat air-soil interface, and (iii) a point target model. Using the method of fundamental solutions to simulate two-dimensional simulations of scalar waves for the direct scattering problem, we systematically study each of these data modeling assumptions. To test and validate these assumptions, we apply principal component analysis to approximately remove ground bounce signals from measurements and then apply Kirchhoff migration on that processed data to produce images. We show that images using this modeled data are nearly identical to those that use simulated measurements from the full direct scattering problem. In that way, we show that this model contains the essential information contained in measurements. Consequently, it provides a theoretical framework for understanding how inherent space/angle limitations affect subsurface imaging systems.

Motivated by the use of unmanned aerial vehicles (UAVs) for buried landmine detection, we consider spectral classification of dispersive point targets below a rough air-soil interface. The target location can be estimated using a previously developed method for ground penetrating synthetic aperture radar involving principal component analysis for ground bounce removal and Kirchhoff migration. For the classification problem, we use the approximate location determined from this imaging method to recover spectral characteristics of the target over the system bandwidth. For the dispersive point target we use here, this spectrum corresponds to its radar cross-section (RCS). For a more general target, this recovered spectrum is a proxy for the frequency-dependence of the RCS averaged over angles spanning the synthetic aperture. The recovered spectrum is noisy and exhibits an overall scaling error due to modeling errors. Nonetheless, by smoothing and normalizing this recovered spectrum, we compare it with a library of pre-computed normalized spectra in a simple multi-class classification scheme. Numerical simulations in two dimensions validate this method and show that this spectral estimation method is effective for target classification.

We propose a method for imaging in scattering media when large and diverse datasets are available. It has two steps. Using a dictionary learning algorithm the first step estimates the true Green’s function vectors as columns in an unordered sensing matrix. The array data comes from many sparse sets of sources whose location and strength are not known to us. In the second step, the columns of the estimated sensing matrix are ordered for imaging using the multidimensional scaling algorithm with connectivity information derived from cross-correlations of its columns, as in time reversal. For these two steps to work together, we need data from large arrays of receivers so the columns of the sensing matrix are incoherent for the first step, as well as from sub-arrays so that they are coherent enough to obtain connectivity needed in the second step. Through simulation experiments, we show that the proposed method is able to provide images in complex media whose resolution is that of a homogeneous medium.

Motivated by applications in unmanned aerial based ground penetrating radar for detecting buried landmines, we consider the problem of imaging small point like scatterers situated in a lossy medium below a random rough surface. Both the random rough surface and the absorption in the lossy medium significantly impede the target detection and imaging process. Using principal component analysis we effectively remove the reflection from the air‐soil interface. We then use a modification of the classical synthetic aperture radar imaging functional to image the targets. This imaging method introduces a user‐defined parameter, δ, which scales the resolution by allowing for target localization with sub wavelength accuracy. Numerical results in two dimensions illustrate the robustness of the approach for imaging multiple targets. However, the depth at which targets are detectable is limited due to the absorption in the lossy medium.

We introduce a dispersive point target model based on scattering by a particle in the far-field. The synthetic aperture imaging problem is then expanded to identify these targets and recover their locations and frequency dependent reflectivities. We show that Kirchhoff migration (KM) is able to identify dispersive point targets in an imaging region. However, KM predicts target locations that are shifted in range from their true locations. We derive an estimate for this range shift for a single target. We also show that because of this range shift we cannot recover the complex-valued frequency dependent reflectivity, but we can recover its absolute value and hence the radar cross-section (RCS) of the target. Simulation results show that we can detect, recover the approximate location, and recover the RCS for dispersive point targets thereby opening opportunities to classifying important differences between multiple targets such as their sizes or material compositions.