## 1 Introduction  
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. Electromagnetic waves at the microwave spectrum allow to get high resolution. That is why over the years a great deal of research has been carried out to tackle the many challenges of subsurface imaging, both in terms of the system and the imaging algorithms [15; 16; 17; 18; 19; 20; 21]. Ground Penetrating Radar (GPR) systems generally work in contact with the air/soil interface. More recently, research has been considering GPRs mounted over airborne platforms as well [22; 23]. This is because a flying GPR can offer the great advantage of inspecting large areas quickly. However, in this framework, the necessity to properly trade-off the system cost and the achievable performance becomes even (with respect to the usual on the ground GPRs) more critical. The most common GPR sensor arrangement is by far the multi-monostatic configuration, where each sensor (or even a single moving sensor) acts simultaneously as transmitter (TX) and receiver (RX). 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. Alternatively, a fleet of sensors can be used. In this case, the system soon becomes too expensive. Therefore, the need for a reduced number of sensors, that in turn should also be relatively cheap, arises. In this regard, a single-view/multistatic configuration seems convenient. Indeed, in this case, only one sensor transmits, whereas the others act like mere receivers. Therefore, they have reduced weight and can be mounted over simple and cheap flying platforms. Of course, synchronization between TX and RX is much more difficult than in the multi-monostatic arrangement, where TX and RX are co-located and share the same electronic system. In order to address this drawback one can resort to some methods used in passive radar technology. In those cases, the receivers estimate the TX parameters, such as the timing, the source position and sometimes also the transmitted waveform, provided that a direct link between TX and RX exists [24; 25]. However, apart from the required additional processing, in this approach the direct link can blind the radar since the field coming from the targets is generally much lower than the direct one, that could saturate the receiver dynamic. 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, hence, 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. In this case, depth information can be disregarded and the main goal is to detect and transversely localize the targets. Accordingly, frequency band is not necessary and single-frequency detection is possible. However, it is assumed that the receivers simultaneously collect the scattered field or at least that the measurement stage is completed within the source coherence interval.