IEEE Geoscience and Remote Sensing Magazine - March 2022 - 261

Note that the resolution formulas in (20) and (21) are derived
under simplified assumptions (e.g., homogenous soil,
rectilinear measurement domains, flat air-soil
interfaces,
and so on). In more general cases, it is very difficult, if not
impossible, to derive closed formulas. Nevertheless, resolution
limits can be estimated numerically with the aid of (19).
Note that the spectral contents achieved in single-view/
multistatic and multiview/multistatic contactless GPR configurations
are derived in a similar way and that their expressions
are reported in [95].
CHALLENGES AND PRACTICAL ISSUES
Here we discuss the main technical challenges related to
contactless GPR imaging. Note that some of them are common
to every GPR application while others are unique to
contactless configurations.
CLUTTER
Clutter is a relevant problem affecting the imaging performance
of GPR systems [1]. The term clutter refers to undesired
signal reflections that fall in the measurement time window
and interfere with the subsurface targets' features.
Direct coupling between Tx and Rx antennas is the main
clutter source for GPR systems. Indeed, when the Tx and
Rx antennas are very close to each other or even if a single
antenna is used (a monostatic configuration), it is not possible
to guarantee a perfect isolation between the Tx and
Rx channels. Consequently, a part of the EM signal couples
directly from the transmitter into the receiver without interacting
with the targets. Direct coupling is an adverse effect
because it masks the response of shallow buried targets. A
possible way to minimize its effect consists of isolating, as
much as possible, the Tx and Rx antennas by placing them
in two separate enclosures. This solution also protects the
antennas from external interferences (e.g., communication
base stations).
In contactless GPRs, direct coupling is no longer a serious
problem because it can be distinguished from the surface
echo [22] as long as the platform height h is increased. Moreover,
in airborne sounding applications where the radar is
very far from the ground and high peak power pulses are
transmitted, the receiver is turned off during transmission
and is activated only after a proper time delay so that the
effect of the direct wave is drastically reduced [62].
Nevertheless, direct coupling is usually an unwanted
signal to be filtered before the imaging task. To this end,
time gating and/or background removal [1] are the most
common filtering strategies applied to raw data. These techniques
are described later in this article as they are also useful
to counteract surface clutter.
Another major clutter source in contactless DL-GPRs
is the signal reflection coming from the air-soil interface.
This signal may completely obscure the one backscattered
by shallower targets, preventing their detection. Ad
hoc hardware solutions and data processing methodologies
have been proposed to mitigate the reflections from
MARCH 2022 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
the air-soil interface. With regard to hardware solutions,
it is worth mentioning the differential GPR configuration
analyzed in [111]. This configuration directly filters the
surface reflection during the survey by recording the difference
of the signals at two Rx antennas, which are located
at the same height above the air-soil interface and are arranged
symmetrically with respect to a central Tx antenna.
However, the differential configuration filters out the lowfrequency
spatial variations of the targets, worsening the
imaging quality.
Data processing schemes that filter reflections from the
air-soil interface have been proposed [1]. The simplest strategy
is time gating, which selects the time interval containing
the signals scattered from targets of interest and sets to
zero the signal outside such an interval. However, the selection
of the optimal time window is a critical issue. Indeed,
when the targets are close to the air-soil interface, the timegating
operation may remove a part of the useful signal.
Another popular filtering approach is background removal
[2]. This procedure assumes that the clutter response
is spatially constant along the measurement direction,
i.e., that the air-soil interface is flat. Background removal
replaces the current trace (A-scan) with the difference between
it and the average value of all the A-scans (or a subset
of A-scans close to the trace of interest) in the radargram
(B-scan). However, background removal also acts on the
signal scattered by the target. As a result, additional compensation
procedures are required to restore the PSF [112].
With regard to surface-clutter filtering, the subspace
projection method should also be considered [113]. This
method assumes that the clutter energy is stronger than
the energy backscattered by the target, and, accordingly, its
contribution is associated with the highest singular value
of the raw data matrix. Therefore, once the SVD of the data
matrix has been computed, the gathered data are projected
onto the subspace spanned by the singular vectors related
to the singular values that are different from the largest
ones. A key point of this method is the estimation of the
clutter subspace dimension, which is often based on the visual
inspection of the curve of the singular values.
Other subspace-based clutter-rejection approaches are
principal component and independent component analyses,
which are based on matrix decomposition using various
constraints in their cost functions [114]. More recently,
morphological component analysis [115], nonnegative
matrix factorization [116], and robust principal component
analysis [117] have also been proposed.
An alternative filtering procedure is the entropy-based
time-gating approach [118]. This method performs an automatic
selection of the time-gating window on the basis
of an entropy criterion. In this way, it is possible to mitigate
the clutter contribution due to the air-soil interface as well
as the unwanted antenna-ringing effects.
Surface clutter is a common problem in every GPR application;
however, it becomes more relevant when radars
are mounted on airborne platforms, such as aircraft,
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