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.
Highlights
Ground Penetrating Radar (GPR) systems generally work in contact with the air/soil interface
We suggest to remedy the reduction of spatial measurements with frequency data [36]
Since the incident field is embodied into the unknown equivalent sources, coherence between the TXs and Rxs is not necessary when single-frequency data are employed. This in principle makes the overall system more cost effective. Even under this model and single-frequency data the study of the number of degrees of freedom (NDF) of the scattered field has revealed that the number of far-zone spatial measurements required to correctly image the equivalent currents may become impractically large, especially for electrically large investigation domains
Summary
The problem of detecting buried targets through electromagnetic waves is a classical inverse scattering problem which is relevant in a number of different applications [1,2] such as civil engineering diagnostics [3,4,5,6,7,8,9], archaeological and geophysical prospecting [10,11], cultural heritage monitoring [12,13], mines and IEDs (improvised explosive devices) detection [14], only to mention a few of them. The point is that for long measurement lines (which are needed to obtain large synthetic apertures in order to obtain high transverse resolution) and large investigated areas, the multi-monostatic arrangement soon requires a huge number of measurement points These can be achieved by a multiple-pass (over the scene under test) strategy but this clearly hinders fast imaging. The present paper is a development of the approach already presented in [26], where we adopted a different point of view and introduced a reconstruction scheme that allows to avoid the need for synchronization and, the direct link blind effect as well This approach is strictly connected to the particular scenario we are interested in, where the targets are assumed buried in close proximity to the air/soil interface (i.e., a few centimeters beneath the air/soil interface just to hide them from sight), as for mine [27] or unexploded improvised device [28] detection.
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