Subsurface detection of shallow targets by undersampled multifrequency data and a non-cooperative source

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