Subsurface Detection of Shallow Targets by Undersampled Multifrequency Data and a Non-Cooperative Source

Abstract

Imaging buried objects embedded within electrically large investigation domains can require a large number of measurement points. This is impractical if long data acquisition time cannot be tolerated or the system is conceived to work at some stand-off distance from the air/soil interface; for example, if it is mounted over some flying platform. In order to reduce the number of spatial measurements, here, we propose a method for detecting and localizing shallowly buried scattering targets from under-sampled far-field data. The method is based on a scattering model derived from the equivalence theorem for electromagnetic radiation. It exploits multi-frequency data and does not require that the transmitter and receivers are synchronized, making the source non-cooperative. To provide a benchmark against which spatial data have to be reduced, first, the number of required spatial measurements is examined by analyzing the properties of the relevant scattering operator. Then, since under-sampling data produces aliasing artifacts, frequency diversity (i.e., multi-frequency data) is exploited to mitigate those artifacts. In particular, single-frequency reconstructions are properly fused and a criterion for selecting the frequencies to be used is provided. Numerical examples show that the method allows for satisfactory target transverse localization with a number of measurements that are much less than the ones required by other methods commonly used in subsurface imaging.

On-Axis Resolution of a Circular Aperture

“…Such formula is in agreement with the one derived in [15]. Note that in the latter paper (32) has been derived by estimating the singular system of the operator A in closed form. Here, we are not able to do that, but we exploit an alternative approach that allows obtaining an approximation of psf evaluated in terms of eigenfunctions v n .…”

“…In array and grid scatterer diagnostics, it suggests the maximum number of elements that can be determined [10,30]. Moreover, N represents the number of independent data [31], a very relevant parameter that allows controlling the occurrence of local minima in Phase retrieval problem [32]. It is estimated as the number of more "significant" singular values of the operator describing the problem under concern.…”

NDF of Scattered Fields for Strip Geometries

“…For PEC objects, the Physical Optics approximation can be invoked for electrically large convex objects. Again, the corresponding scattering operator is linear with the same kernel as in [1], and an unknown distributional function representing the object shape [22]. Therefore, the whole discussion can be extended promptly to the PEC case.…”

“…The electromagnetic waves can be applied to investigate hidden or remote regions. The imaging algorithms based on inverse scattering methods are appropriate for a broad range of applications, such as medical imaging and subsurface imaging [1,2], ground-penetrating radar (GPR) [3][4][5][6], radar imaging, and military applications [7,8].…”

On the Introduction of Canny Operator in an Advanced Imaging Algorithm for Real-Time Detection of Hyperbolas in Ground-Penetrating Radar Data

“…While the goal of various quantitative microwave imaging techniques for GPR applications (including APEX and SPOT-GPR) is to detect, localize and characterize discrete buried objects, other approaches aim at an overall electromagnetic reconstruction of the underground structures, and more specifically at a qualitative or quantitative estimation of the geometrical distribution of the physical properties of media (dielectric permittivity, electric conductivity) in the subsurface [35,36]. Such methods are promising for the analysis of radargrams obtained in highly heterogeneous environments [37].…”