1226 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 13, NO.

9, SEPTEMBER 2016

Comparative Analysis of Two Approaches for

Multipath Ghost Suppression in Radar Imaging
G. Gennarelli, G. Vivone, P. Braca, F. Soldovieri, Senior Member, IEEE, and M. G. Amin, Fellow, IEEE

Abstract—Radar imaging is typically based on linear models of

the electromagnetic scattering phenomenon. These models are ro-
bust and computationally efficient, but do not account for mutual
interactions among targets in the scene and between the targets
and the surrounding environment. As a result, the radar images
are characterized by spurious targets, i.e., multipath ghosts, which
appear at positions where no physical targets exist. In this letter,
we compare two key approaches for clutter suppression. The first
approach applies multiplicative fusion of the images correspond-
ing to subapertures of the deployed array, whereas the second
approach is based on coherence factor filtering, which enhances
the image quality by suppressing low-coherence features. We as-
sess the performance of these two methods in terms of imaging
and detection capabilities. Numerical results based on synthetic
data are reported to support the comparative analysis. Fig. 1. Geometry of the problem. Multipath phenomena occur in the investiga-
tion region D due to the interactions among the targets.
Index Terms—Image fusion, multipath ghosts, radar imaging.
Strategies to mitigate, or effectively remove, multipath
I. I NTRODUCTION ghosts are also of interest. They become crucial in the absence
of any prior information about the scene or its major scatterers

T ARGET detection and localization based on knowledge

of the scattered electromagnetic (EM) field remain the
primary goals in radar imaging applications. Most radar imag-
and under strong mutual target interactions. Ghost mitigation
strategies can be based on ghost phase delays of the radar
returns [12], the aspect-dependent characteristics of multipath
ing approaches are founded on linearized models of the EM ghosts by subaperture imaging [13]–[15], or the analysis of
scattering phenomena [1]. These models allow a qualitative range Doppler smearing due to multipath [16]. Recently, it has
description of the targets (i.e., location and approximate shape) been shown that multipath ghosts can be effectively mitigated
by means of robust and computationally efficient data process- by a multiplication fusion of subarray images [17]. However,
ing algorithms. Several data processing strategies have been this approach suffers from the drawback of suppressing weak
proposed in the literature [1]. scattering targets, thereby impairing the image interpretations.
Linear models describe only direct scattering [2], thereby Another popular approach is the coherence factor (CF) filtering
neglecting the scene multipath effects related to target-to-target that mitigates clutter by suppressing its low-coherence features
and target-to-environment interactions. These multipath contri- [18], [19]. These two approaches have never been compara-
butions produce spurious objects in the reconstructed images, tively assessed.
thus increasing clutter and false alarms. Multipath signals and Building on the results reported in [17], this letter presents
their ghosting effects can be exploited [3]–[11], possibly en- a performance evaluation of the aforementioned approaches
hancing the signal-to-clutter ratio and the spatial resolution [5], for clutter rejection. The multiplicative subarray image fusion
[8]. These methods, which assume prior knowledge of the scene (MSIF) approach is compared with the CF filtering approach by
layout and model multipath propagation, have been proposed in resorting to suitable image performance metrics. The classical
the context of through-wall radar imaging and urban sensing. ordered statistic constant false alarm rate (OS-CFAR) detector
[20] is applied to compare the strategies in terms of target
Manuscript received March 9, 2016; revised April 19, 2016; accepted June 2, detection rate (DR) and false alarm rate (FAR).
2016. Date of publication June 23, 2016; date of current version August 5,
2016.
G. Gennarelli and F. Soldovieri are with the Institute for Electromagnetic II. R ADAR I MAGING M ODEL AND I NVERSION A PPROACH
Sensing of the Environment, National Research Council of Italy (CNR), 80124
Napoli, Italy (e-mail: gennarelli.g@irea.cnr.it; soldovieri.f@irea.cnr.it). Consider the 2-D geometry depicted in Fig. 1. Without loss
G. Vivone and P. Braca are with the North Atlantic Treaty Organization of generality, the background is assumed to be free space.
Science and Technology Organization Centre for Maritime Research and Ex- In general, more complex scenarios can be accounted for by
perimentation, 19126 La Spezia, Italy (e-mail: gvivone@unisa.it; paolo.braca@
cmre.nato.int). resorting to pertinent EM modeling [1], [2]. Several targets,
M. G. Amin is with the Center for Advanced Communications, Villanova supposed metallic, are located in the investigation domain D,
University, Villanova, PA 19085 USA (e-mail: moeness.amin@villanova.edu). which is probed by an antenna array (either a synthetic or
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org. a physical aperture) directed along x and covering the inter-
Digital Object Identifier 10.1109/LGRS.2016.2577715 val Γ of length Lx . The array operates in a multimonostatic
1545-598X © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
GENNARELLI et al.: COMPARATIVE ANALYSIS OF TWO APPROACHES FOR MULTIPATH GHOST SUPPRESSION 1227

mode, i.e., the scattered field is collected at the same location For convenience, I MSIF is normalized with respect to its
of the source. A wideband operation in the frequency range maximum value. As shown in [17], the MSIF approach defined
Ω = [ωmin, ωmax ] is considered. Each source is modeled as a by (3) offers the possibility to attenuate spurious targets; how-
filamentary electric current directed along the y-axis (transverse ever, weak objects may be also suppressed.
magnetic polarization), so that the problem at hand is scalar.
The source/receiver positions are denoted by rs , and r is a B. CF Filtering Approach
generic point in D. Fig. 1 illustrates multipath phenomena
arising in the presence of several close targets. CF filtering is an imaging tool that has been first applied in
Under physical optics approximation, a linear scattering ultrasonic imaging [18] and recently employed in through-wall
model is established [17], [21], i.e., radar imaging [19]. CF measures the coherence of signals scat-
 tered from a generic point in the investigation domain D and is
Es (rs , ω) = G(rs , r, ω)Ei (rs , r, ω)γ(r)dτ = Lγ (1) defined as the ratio between the total coherent power received
by the radar aperture to the total incoherent power. Define
τ
ωmax
where Es is the scattered field (datum), G is the free-space
Green’s function, Ei is the incident field in D, and γ is a ym (r) = Es (r sm , ω)ej2k|r−rsm | dω (4)
distribution (unknown) supported over τ = ∪i τi , i.e., the union ωmin
of target contours τi . The operator notation has been introduced
as the downrange profile of the scattered field Es , where M is
in (1), where the linear operator L : X → Y maps the space of
the total number of measurement points located at rsm , m =
unknown X into data space Y .
1, . . . , M . CF is expressed as
Different methods can be applied to invert the problem (e.g.,
 2
see [1] and [22]). In this letter, we consider the common  M 
 m=1 ym (r)
inversion scheme based on the adjoint operator L∗ , i.e., , r ∈ D.
CF(r) =  (5)
M M m=1 |ym (r)|
2

γ = L∗ Es (2)
The spatial map defined by CF(r) varies from zero to one
which is basically equivalent to beamforming or matched filter- and provides information about the low- and high-coherence
ing. The spatial map defined by the magnitude of γ is referred regions in the investigated domain. The CF-enhanced image
as the tomographic image and denoted by I. I CF is obtained by applying the CF function to the tomographic
As shown in [17], the scattered field is the superposition image I provided by adjoint inversion, i.e.,
of direct scattering contributions and multipath terms. The
former are responsible for the reconstruction of true targets in I CF (r) = CF(r)I(r) r ∈ D. (6)
the scene, whereas the latter are associated with false targets.
Multipath ghosts are typically defocused with respect to the According to (6), features with low coherence such as mul-
true targets and are located at positions where no physical tipath ghosts are suppressed, or significantly attenuated, in the
target exists. Most notably, according to [13]–[15], multipath image. Note that, similar to the multiplicative fusion, CF could
ghosts exhibit aspect-dependent characteristics. Thus, a differ- be also calculated using the same N subarrays, where the
ent behavior in ghost reconstructions (i.e., location and shape) coherent result from each subarray is then combined coherently
is observed when partitioning the radar aperture into smaller and noncoherently to form a composite CF. However, this
subarrays. This enables ghost suppression by fusion of subarray approach reduces the noncoherent terms in the denominator and
images [17]. is, therefore, inferior to the form in (5).

III. M ULTIPATH G HOST S UPPRESSION S TRATEGIES C. Imaging Performance Metrics

AND P ERFORMANCE C RITERIA
Two different metrics are used to compare the performance
This section discusses the two multipath ghost mitigation of the two strategies in terms of image quality [23]. The first
approaches and defines performance criteria for comparison. metric is the improvement factor (IF) in the target-to-clutter
ratio (TCR), which is defined as
 
A. MSIF Approach TCRout
IF = 10 log10 (7)
Following [17], the radar aperture is partitioned into TCRin
N subarrays, and a tomographic image In is obtained from each
where TCRin,out = P tin,out /P cin,out , and P t and P c denote
subarray data set via (2). Then, a composite ghost-free image
the average target and clutter powers, respectively. The sub-
I MSIF is obtained by a pixel-by-pixel multiplicative fusion of
script “in” refers to the image when only adjoint inversion
magnitude images related to each subarray [23], i.e.,
is carried out according to (2). The subscript “out” refers to

N the image achieved after the application of a ghost mitigation
I MSIF (r) = In (r), r ∈ D. (3) strategy (MSIF or CF). Note that the IF parameter describes the
n=1 enhancement in the overall image.
1228 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 13, NO. 9, SEPTEMBER 2016

The second figure of merit, more suitable for weak scatterers,

is the target improvement factor (TIF)
 
P tout
TIF = 10 log10 (8)
P tin
which quantifies the improvement of the target power P t. Since
the goal is to analyze performances in known scenarios, the IF
and TIF parameters are evaluated over the regions of interest
(RoIs) containing the true targets. It is feasible to compute the
target and clutter powers involved in (7) and (8). Specifically,
the average power in a target or a clutter region Rt,c of the
composite image I is defined as

1  2
Qt,c
Pt,c = I (r), r ∈ Rt,c (9)
Qt,c q=1 q Fig. 2. Simulated scenario: (blue circles) measurement points, (red rectangle)
investigation domain, (black circles) targets, and (green rectangles) RoI.
where Qt,c is the number of pixels belonging to Rt,c .

D. Detection Performance
The classical OS-CFAR detector [20] is implemented to eval-
uate the detection performance of the MSIF and CF strategies.
Such a detector works as follows. The square amplitude of
each pixel in a tomographic image is compared to a threshold,
which depends on the estimated noise level and nominal PF A .
The observations in the reference window are sorted to form a
sequence in ascending numerical order {I(1) , I(2) , . . . , I(Nc ) },
where Nc is the number of cells in the reference window.
The kth-order statistic I(k) is selected as representative of
Fig. 3. Relative amplitude (dB) of the tomographic image achieved by adjoint
the interference level, and the threshold is set as Th = αI(k) . inversion when SNR is 0 dB. Red arrows denote multipath ghosts.
For a square-law detector and additive white Gaussian noise
(AWGN) on the real and imaginary parts of the complex image
reconstruction, the clutter in the tomographic image I has an The numerical tests exploit synthetic data generated by the
exponential distribution. As a result, the constant α is evaluated GPRmax2D solver [24]. The scattered field in the frequency
from the nominal PF A as domain is computed from time-domain data after a time-gating
operation to remove direct coupling between transmitting and
Nc ! (k − 1)!(α + Nc − k)! receiving antennas. Finally, the frequency domain data are
PF A = k . (10)
k!(Nc − k)! (α + Nc )! corrupted by AWGN.
The receiver operating characteristic (ROC) curves are eval- The tomographic reconstruction depicted in Fig. 3 is ob-
uated to examine the performance of the ghost mitigation tained by standard adjoint-based inversion of data collected by
approaches. To this end, the nominal PF A is varied, and so the entire array. The signal-to-noise ratio (SNR) on the scattered
is the threshold Th , which implies a simultaneous variation field is assumed to be 0 dB. As can be seen, high-intensity spots
of DR and FAR. As done in [23], the DR is computed as the appear in correspondence of the upper edge of the targets since
percentage of pixels detected in the RoI, i.e., where true targets they are not penetrable. However, due to multiple scattering, the
are present, whereas the FAR is calculated as the percentage of image is cluttered by lower intensity artifacts, which appear as
pixels detected in the clutter region. spots located among the targets and at greater downrange (see
red arrows in Fig. 3).
The reconstructions in Fig. 4 are obtained by applying the
IV. N UMERICAL R ESULTS
MSIF approach. To this end, the original array is partitioned
The measurement array, which is depicted in Fig. 2, covers into N contiguous and nonoverlapping subarrays. In particu-
the interval [−1.5, 1.5] m, and the spacing between the mea- lar, we report the images achieved when N = 2 (left panel),
surement points is fixed at 0.0375 m (81 measurement points). N = 3 (center panel), and N = 4 (right panel). It is evident
The operating frequency range of the system is [0.5, 1.5] GHz, that the images are much less cluttered than in Fig. 3 and
and a frequency step of 50 MHz is considered for data inver- multipath ghosts and noise are significantly attenuated. For
sion. The investigation domain D = [−1.0, 1.0] × [0.5, 2.0] m2 N = 2, the three targets are clearly distinguishable, and only
is discretized into square image pixels with a size of 0.05 m. some residual clutter is present. However, as the number of
The scene is populated by three metallic cylinders having a subarrays increases (N > 2), the clutter is totally suppressed,
radius of 0.1 m and centered at (−0.5, 1.25), (0, 0.75), and (0.5, but the response of the two far targets is weakened so that
1.25) m, respectively. their visual identification becomes difficult for the considered
GENNARELLI et al.: COMPARATIVE ANALYSIS OF TWO APPROACHES FOR MULTIPATH GHOST SUPPRESSION 1229

Fig. 4. Relative amplitude (dB) of the tomographic images achieved by adjoint inversion and MSIF when SNR on data is equal to 0 dB. (Left panel) N = 2
subarrays. (Center panel) N = 3 subarrays. (Right panel) N = 4 subarrays.

Fig. 6. Image performance metrics (dB) versus SNR averaged over 200 Monte
Carlo trials. (Left panel) IF. (Right panel) TIF.
Fig. 5. Relative amplitude (dB) of the tomographic image achieved by adjoint
inversion and CF filtering when SNR on data is equal to 0 dB.
The curves, showing the average TIF versus SNR, are re-
dynamic range. By increasing this range, all targets can be ported in the right panel in Fig. 6. A behavior almost indepen-
identified, but with amplified clutter. dent of SNR is clearly observed for each strategy. This graph is
The image in Fig. 5 is obtained by adjoint inversion followed informative since it underscores the fact that, for a fixed SNR,
by the application of the CF approach. It can be observed the target response achieved via MSIF approach degrades as
that most of the clutter in Fig. 3 is suppressed, except for the number of subarrays increases. The decreasing trend at low
some residual artifacts. On the other hand, the real targets are SNR values is justified by realizing that the power in the target
clearly discernible, unlike for the MSIF approach with N = regions after image fusion is almost independent of SNR; con-
3, 4. Moreover, despite the symmetrical scene, lateral targets versely, when only adjoint inversion is performed, the increase
have different amplitudes because data are affected by AWGN, in power is an effect of the higher noise level. As a result, the
which is not spatially symmetric. ratio defined by (8) decreases. The CF filtering provides TIF
In order to disengage from the specific realization of the values nearly intermediate between those achieved via MSIF
AWGN, 200 Monte Carlo trials are performed for SNR values approach for N = 2 and N = 3.
equal to −10, −5, 0, 5, and 10 dB. For each value, the imaging Finally, the detection performance is assessed from the ROC
performance metrics, which are introduced in Section III-C, are of the OS-CFAR detector. The 75th percentile is chosen to fix
computed and averaged over the trials. the threshold Th [20]. The reference and guard window sizes
The left panel in Fig. 6 displays the average IF versus are 11 × 11 and 7 × 7 pixels, respectively. The DR and the
SNR for both the MSIF and CF filtering approaches. For the FAR are averaged over the Monte Carlo trials.
MSIF approach, IF is computed for three different numbers of The ROC curves in the left, center, and right panels in
subarrays (N = 2, 3, 4). For a fixed number of subarrays, IF de- Fig. 7 refer to SNR values equal to −10, 0, and +10 dB,
creases with SNR, with the more favorable situation (higher IF) respectively. It is shown that, when standard adjoint inversion
occurring when N = 4; this behavior is consistent with (7). is performed and no clutter rejection strategy is applied, the
Indeed, it is observed from the numerical results that TCRout achievable DRs are highly dependent on the noise level of the
is weakly dependent on the SNR, whereas TCRin , which is data and increase with SNR for a fixed FAR. This result has a
based on adjoint inversion, significantly degrades as the SNR physical justification, since targets are less detectable when data
decreases. are severely corrupted by noise and clutter. It is also shown that
The CF filtering exhibits a similar trend versus SNR. How- the MSIF approach significantly improves the DR with respect
ever, the achieved improvement in TCR is lower than that to standard adjoint inversion. This is particularly evident from
of the MSIF approach. This behavior is consistent with the the results achieved for SNR values equal to −10 and 0 dB. It
tomographic image in Fig. 5, which highlights the presence of is important to note that the DR values achieved with MSIF and
a slightly larger residual clutter with respect to the images in CF filtering approaches are comparable and almost independent
Fig. 4. Note that, for high SNRs, the CF filtering has a similar of the SNR. This is due to the fact that the TCR and the
performance to the MSIF approach with N = 2. targets’ power, after the application of MSIF and CF filtering,
1230 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 13, NO. 9, SEPTEMBER 2016

Fig. 7. ROC curves of the OS-CFAR detector for adjoint inversion, MSIF approach (N = 2, 3, 4), and CF filtering strategies. (Left panel) SNR = −10 dB.
(Center panel) SNR = 0 dB. (Right panel) SNR = +10 dB.

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