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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 14, NO. 2, FEBRUARY 2017
Target Extraction and Imaging of Maritime
Targets in the Sea Clutter Spectrum
Using Sparse Separation
Masoud Farshchian
Abstract— Detection and imaging of endoclutter maritime
targets is a difficult problem, because the signal return of the target and the clutter overlap in both Doppler frequency and time.
Consequently, traditional Doppler filtering is severely limited in
terms of extracting the target signature for further processing.
This letter proposes a new sparsity-based Doppler filtering and
extraction paradigm for maritime radar where the different
backscattered signals are separated in the endoclutter region
based on their Doppler bandwidths rather than their Doppler
frequencies. The novelty of this letter is successful extraction of
the target profiles in the endoclutter region using the application of morphological component analysis with time–frequency
transforms. Illustrative results of the proposed approach for boat
Doppler profile extraction and inverse synthetic aperture image
formation outperform traditional range-Doppler processing in
endoclutter. The method represents a new paradigm for target
detection and imaging in sea clutter.
Index Terms— Inverse synthetic aperture radar, radar detection, radar imaging.
I. I NTRODUCTION
ADAR target detection using Fourier Doppler filtering
is optimal for a constant-velocity point target in the
exoclutter region (when the target’s Doppler profile has a
different frequency support than the Doppler spectrum of
the clutter) [1]. However, the detection performance of the
same technique degrades significantly in the endoclutter region
(when the target’s Doppler frequencies overlap with the
Doppler spectrum of the clutter) relative to a constant false
alarm rate (CFAR). Therefore, other signal processing methods
to differentiate endoclutter targets from the clutter background
are needed.
New approaches using adaptive filter detectors have been
proposed (for an extensive review see [2]). In general, these
adaptive filter detectors rely on first whitening the clutter using
covariance estimates derived from secondary samples that are
ideally not contaminated by the target and are representative
of the cell under test (CUT). Afterward, a test statistic for
target detection for each assumed Doppler frequency of the
target is calculated and compared with a threshold. A variety
of these types of detectors have recently been proposed using
the three combinations of [2]: 1) an approximate or exact
generalized likelihood ratio test (e.g., Kelly detector, adaptive
R
Manuscript received April 1, 2016; revised September 14, 2016; accepted
November 29, 2016. Date of publication December 28, 2016; date of current
version January 19, 2017.
The author is with Empyreal Waves LLC, Fairfax Station, VA 22039 USA
(e-mail: mfarsh@gmail.com).
Color versions of one or more of the figures in this letter are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/LGRS.2016.2636253
matched filter detector, adaptive normalized matched filter
detector, and so on); 2) proposed different clutter models
(especially spherically invariant random processes models) [3];
and 3) different techniques for the estimation of the timevarying clutter covariance matrix. Based on the conclusion of
Carretero-Moya et al. [2], these methods have been shown to
be unreliable due to their large false alarm deviation and probability of detection losses for small target detection. A major
reason for this degradation is the estimated covariance matrix
whose statistics might differ greatly from the CUT [2], [4].
The unreliable estimates are due to the nonstationarity of
sea clutter itself [2]. Consequently, as pointed out in [2], the
approaches of these methods may not be appropriate for the
detection of targets in sea clutter. Carretero-Moya et al. [2]
point out that: the main conclusion of this letter is that
CFAR detection in heterogeneous high-resolution sea-clutter
is clearly still an open problem.
We propose a novel approach for endoclutter target detection. The proposed nonlinear filtering technique, new in the
maritime radar framework, allows signals to overlap in time
and Doppler frequency, yet separates (decomposes) them
based on their differing Doppler bandwidth [5] rather than
Doppler frequency (as in traditional range-Doppler processing). Furthermore, our emphasis is to perform such a separation (decomposition) without utilizing any adjacent or target
cell covariance estimates or probability distributions [2], [4].
As will be explained and demonstrated by the experimental
results based upon real measured data, the method of this letter
is well-suited for discriminating signals based on their Doppler
bandwidth and does not require the covariance estimate of the
clutter. The ability to extract target signatures in endoclutter is
a salient feature of the approach of this letter compared with
the adaptive filtering algorithms that assume quasi-stationarity
of sea clutter [2].
Morphological component analysis (MCA), first applied
to image processing, is a recent sparsity-based separation
technique [6] that decomposes a signal mixture into several
components where the components are assumed to be sparse
in different transform domains [6]. Two requirements for the
effective application of MCA are: 1) the sparsifying dictionaries and 2) the optimization algorithm. In this letter—as far as
we are aware for the first time—we apply MCA to the radar
problem of: 1) boat Doppler profile extraction in endoclutter
and 2) inverse synthetic aperture radar (ISAR) endoclutter
image formation. In particular, our objective is to work on
the raw I /Q data and separate the target from the sea clutter
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FARSHCHIAN: TARGET EXTRACTION AND IMAGING OF MARITIME TARGETS IN THE SEA CLUTTER SPECTRUM
using their different Doppler bandwidths. The novelty here is
the application of MCA with the specific dictionaries for the
successful extraction of maritime targets.
An important emphasis of this letter is the utilization of
dictionaries that lead to the sparsification of the target in
the endoclutter and the exoclutter regions. The dictionaries used in this letter are the invertible short-time Fourier
transform (STFT) with different window-lengths. The first
application of such dictionaries in radar was the attenuation of Doppler-steaks due to transient noise and target spread for low frequency radar [7]. In [8], an MCA
approach using the resonance-based dictionaries [9] was
applied to the maritime discrimination of boats from bird flock
(bird clutter) in sea clutter. It was noted that the spectrum of
the bird flock has a broad Doppler spectrum while that of
the boat has a narrow Doppler spectrum. The recent paper by
Nguyen and Al-Ashwal [10] also utilize the resonance-based
dictionary [9] to improve exoclutter detection of boat targets
in sea clutter. However, despite the improved results discussed
in [8] and [10], the utilization of the resonance-based dictionaries in [8] and [10] is not suited for the endoclutter region.
This is because both the target and the clutter will have a
small number of oscillations. Consequently both signals will
be sparsified by the same low-resonance dictionary (which
sparsifies signal with small number of oscillations as opposed
to the high-resonance dictionary) [9], leading to poorer separation. Obviously, this is not the case for exoclutter targets
which will have a sparse high-resonance (large number of
oscillations) component, and subsequently can be successfully
separated from low-resonance signals [8], [10]. Since the focus
of this letter is on endoclutter targets rather than exoclutter
targets, the STFT is preferable to constant-Q transforms used
in [8] and [10].
In Section II, a brief overview of MCA [6] is provided.
The dictionaries in this letter are the STFT frames which
are discussed in Section III. In Section IV, we apply the
MCA approach to extract a small radar cross section (RCS)
boat from a high sea state clutter, and also to ISAR image
formation. Section V summarizes the contributions of this
letter and future research directions.
II. M ORPHOLOGICAL C OMPONENT A NALYSIS
We utilize the MCA approach to extract a narrow-band
component from a wideband background over all Doppler
frequency bins even when both components overlap in time
and frequency. Given an observed signal x = x1 + x2 , where
x1 , x2 ∈ C N represent the component signals of interest,
the goal of MCA is to estimate x1 and x2 individually. We
denote by ∗ that the Hermitian transpose of operator . We
assume that the over-complete transforms ∗1 and ∗2 enable
sparse representations of the vectors x1 and x2 , with coefficient
vectors w1 ∈ C M1 ×K 1 and w2 ∈ C M2 ×K 2 , respectively. Note
that ∗i has its domain as an Mi × K i sized vector (which can
be written as a matrix) and its range as an N sized complex
vector. That is, ∗i : C Mi ×K i → C N . A sparse representation
of a signal is one where a small number of representation
coefficients account for most of the signal energy. According
to one form of MCA, given x, we estimate x1 and x2 by
233
solving the following minimization problem:
arg min λw1 1 + (1 − λ)w2 1
(1a)
∗1 w1
(1b)
w1 ,w2
such that x =
+ ∗2 w2 .
Here, λ is a positive scalar regularization parameter although
it can readily be extended to a vector to emphasize different
atoms within a dictionary. One method to obtain the sparse w1
and sparse w2 coefficients is the split augmented Lagrangian
shrinkage algorithm [11] as described in [9] and is also widely
known as the alternating direction method of multipliers
optimization [11]. The method relies upon breaking a large
optimization problem into smaller subproblems that can be
solved more easily. An algorithm to minimize (1) is given by
[9] and reproduced here for completeness
initialize: μ > 0, d, w
(2a)
w1
d1
0.5λ/μ
d1
u1
← soft
+
,
−
(2b)
u2
w2
d2
d2
0.5(1 − λ)/μ
u1
1 1
d1
←
x − ∗1 ∗2
(2c)
d2
u2
2 2
d
u
w1
← 1 + 1
(2d)
w2
d2
u2
repeat
where soft(y, T ) is the soft-threshold rule with threshold T
defined by
soft(y, T ) = y max(0, 1 − T /|y|),
y ∈ C, T ∈ R+ .
(3)
Because of the high clutter-to-noise ratio (measured
above 25 dB) in the experimental data, we have used an
equality constraint in (1b) leading to signal representation
rather than signal approximation (as in other forms of MCA).
III. A PPROPRIATE D ICTIONARY
Choosing the appropriate dictionary i is one of the main
requirements in the successful application of MCA. Under the
narrow-band assumption, the baseband return signal r (t) of a
transmitted signal s(t) for a constant point scatterer moving
with a constant velocity is
r (t) = αs(t − τ ) exp(i ωd (t − τ ))
(4)
where ωd is the Doppler frequency, τ is delay, and α is a constant that is proportional to the RCS. Even with a nonconstant
RCS, the amplitude modulation of the RCS does not induce a
large Doppler bandwidth relative to sea clutter. Consequently,
the narrow-band signal of a point target is sparsely represented
with a few coefficients for a long-window STFT or discrete
Fourier transform (DFT). In contrast, an accurate model for
the background sea clutter is not available. Since sea clutter
returns from the ocean are scattered from a distributed surface
which is undergoing complex and dynamic wave motion, sea
clutter has a broad time-varying spectrum. Qualitatively (as is
apparent from the STFT), and quantitatively, the mean Doppler
bandwidth of the sea clutter is much wider than those of point
scattered targets [5] (also see Fig. 4 where the clutter and target
Doppler bandwidths are about 200 and 10 Hz, respectively).
A wideband signal which is equivalent to a more transient
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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 14, NO. 2, FEBRUARY 2017
signal (e.g., sea clutter and spray generated by the ocean) is
more sparsely represented with a short-window STFT than a
long-window STFT.
We can write the discrete STFT S(k, m) as
R−1
(5)
S(k, m) = DFT M x(n − Lm)v(n)|n=0
, 0 M−R
where m is the time index, k is the frequency index, R is
the window-length, L is the temporal hop, and M is the DFT
length. Both the overlap factor of R/L, where 1 ≤ L ≤ R, and
frequency sampling of M > R leads to more STFT coefficients
than signal values N, where the length of x(n) is N. We note
that K i in ∗i is equal to N/L. In order to make the adjoint
of the forward STFT equal to its left inverse, we start with (5)
and denote s(n, m) as the inverse discrete Fourier transform
(IDFT) of S(k, m). Multiplying by the symmetric window v(n)
gives
s(n, m) = IDFT M (S(k, m))v(n) = x(n − Lm)v 2 (n).
(6)
Substituting p = n − Lm, we sum over the overlapping blocks
to obtain the original signal provided v(n) satisfies
x( p)v 2 (Lm + p) = x( p).
(7)
Fig. 1.
ISAR image before and after MCA.
TABLE I
ISAR R ADAR D ESCRIPTOR
m
We have used a sine window which satisfies the abovementioned relationship [12]. Consequently, we have the following tight frame relationship between and its adjoint:
∗ x = x.
(8)
Now, the algorithm of the Section II can be applied.
TABLE II
CSIR R ADAR D ESCRIPTORS
IV. A PPLICATION OF MCA TO S MALL
B OAT D ETECTION AND ISAR
A. Application to ISAR
ISAR obtains a high-resolution image of an object by
coherently processing pulses that are produced as the object of
interest rotates [13]. In high sea states, and for boats producing
turbulent sprays due to dynamic interactions with the sea,
the effects on the Doppler spectrum of the spray from the
boat and sea clutter also appears in individual range-cells.
These nontarget features adversely affect the recognition of
the object. Consequently, the full classification potential of
ISAR may not be realized in this scenario. Since the reflections
from the boat are narrowband relative to the nonstationary sea
clutter and spray, the separation of the wideband and narrowband components can be performed via MCA. Furthermore,
the wideband components that are extracted can be used as
an additional feature of a classifier as each boat may have
different Doppler profiles generated from its turbulent spray.
The NRaD linear frequency modulated radar is a wideband, coherent, high-range resolution radar that operates at
X-band [14]. Table I summarizes the radar parameters.
The radar is located on the west side of Point Loma,
San Diego, CA, overlooking the Pacific Ocean, at approximately 120 ft above sea level. The experiment here used a
utility boat. The raw range-Doppler data set was first rangealigned using a cross-correlation algorithm [13]. Afterward,
MCA was applied to the complex 2-D range-Doppler matrix
on a range-cell-by-range-cell basis with 100 iterations per
range-cell. A regularization value of λ = 0.8 was chosen
with STFT window-lengths of R1 = 4 and R2 = 128, and
a temporal hop of L = 1 for each dictionary. Fig. 1 (in dB
scale and the Doppler axis is normalized by the pulse repetition
frequency (PRF)) shows the results of separating the spray/sea
clutter (“wideband”) from the (“narrowband”) utility boat.
The additional clarity of the narrow-band component allows
for further application of motion compensation algorithms
to enhance the ISAR images while the wake/spray can be
used as an additional feature to reduce misclassifications.
It should be noted that the MCA approach is drastically
different than thresholding. Fig. 2 shows the narrow-band and
wideband component of the spectrogram of the range-cell
before and after separation (decomposition). We note that there
are high amplitude wideband components (from the spray)
that were correctly separated into the wideband stream and
high amplitude narrow-band components that were correctly
separated into the narrow-band stream. In a threshold method,
both high amplitude components (narrowband and wideband)
are selected which results in no separation between target
scatterers and clutter.
FARSHCHIAN: TARGET EXTRACTION AND IMAGING OF MARITIME TARGETS IN THE SEA CLUTTER SPECTRUM
Fig. 2.
Fig. 3.
SCR gain as a function of λ for data set 2.
Fig. 4.
Doppler spectra of the target cell.
235
Spectrogram before and after MCA.
B. CSIR Data
We also applied the new extraction algorithm to several
measured S-band and X-band data sets provided by The
Council for Scientific and Industrial Research (CSIR) in
South Africa [15] with consistent results. Unlike the ISAR
results, there is no range-migration or rotational diversity in
our processing interval, and we focus solely a Doppler profile
of the target. Here, we mention only one experiment in detail
where the target is slowly drifting. We denote SCRi and
SCRo as the input and output signal-to-clutter ratio (SCR)
before MCA and after the MCA narrow-band component,
respectively. Similarly, MCRi and MCRo are the input and
output maximum clutter ratio (MCR) (maximum clutter cell
power divided by the average power of all clutter cells) before
and after MCA, respectively. We denote the separation metric
values between the target and maximum clutter cell before and
after MCA as i = SCRi − MCRi and o = SCRo − MCRo ,
where the subtraction is done in the dB scale. It should be
noted that SCRi is used in traditional radar processing such
as CFAR detectors [1] and its small value is the reason for
the difficulty of detection of small targets in the endoclutter region. The CSIR data set “TFC15-007” (summarized
in Table II) was examined as an example of an endoclutter
target. The target is a rigid inflatable boat with an RCS of the
range 1–5 m2 . The target plus clutter cell was located
at range-gate 20 (roughly corresponding to 3285 m).
For display comparisons, we use a clutter range-gate
number 47 (roughly 3690 m) as a representative of a clutter
cell. For the MCA separation, we chose a window-length of
R1 = 32 samples for the wideband dictionary and a windowlength of R2 = 2048 samples for the narrow-band stream
(corresponding to 0.41 s). An overlap of 80% was used for the
STFT of both dictionaries. A four second portion of the datastream was taken for analysis and data processing. It should be
noted that the MCA can be applied to different data lengths.
However, we experimented with a longer data length in order
to analyze the variation of the MCA output over a few seconds.
In Fig. 5, from the top to the bottom, the spectrogram of a
portion of the pre-MCA data, the post-MCA wideband spectrogram, and the post-MCA narrow-band spectrogram are shown,
respectively, for the clutter cell and the value of λ = 0.18.
Beyond 100 iterations of the algorithm to separate the data
into a narrow-band and wideband component, there was no
significant improvement seen in the quality of the separation.
In Fig. 4, from the top to the bottom, the spectrogram of
a portion of the pre-MCA data, the post-MCA wideband
spectrogram, and the post-MCA narrow-band spectrogram are
shown for the target plus clutter cell for the value of λ = 0.18.
For both Figs. 4 and 5, a window-length of R = 1024 was used
to display the spectrograms of the narrow-band and wideband
streams. Fig. 3 shows SCRi , SCRo , MCRi , and MCRo for
this experiment. Fig. 3 shows that a significant improvement
of 4.76–40.7 dB for the average SCR can be obtained when
λ is between 0.10 and 0.25. Similarly, i = 0.43 dB, while
the maximum value of o , which occurs at λ = 0.13, is equal
to 34.73 dB. These numbers are due to the fact that MCA
separates the two signals based on their Doppler bandwidth.
That is, using the new algorithm, we have increased the
separation of the target power relative to the maximum clutter
power in the narrow-band component. The increase in o
relative to i suggests that the false alarms can be reduced
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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 14, NO. 2, FEBRUARY 2017
covariance-based adaptive filter methods [2]. It should be
mentioned that for ultrawideband radar, the resonance-based
dictionaries may also be suitable due to the time scaling of
the returns. Comparison of the STFT approach to the resonance and other dictionaries for narrow-band and wideband
radar detection, discrimination and imaging of exoclutter and
endoclutter targets with varying trajectories is left as a future
research topic. It should be noted that the MCA approach
allows for several different dictionaries from different transform families to be combined. Given the reasons and results
of this letter, we believe the image-processing-based MCA
approach is a promising alternative technique to covariancebased adaptive filter methods for nonstationary radar clutter,
and future work will compare these two different approaches.
R EFERENCES
Fig. 5.
Doppler spectra of a clutter cell.
by processing the narrow-band component in the detection
chain rather than the mixed component. The optimal value of λ
may depend on several factors, including the observation time
for processing, the persistence of the target and the clutter,
the PRF of the data, and the Doppler bandwidth (which is
determined by environmental conditions). However, even if the
optimal value of λ is not chosen, significant gains are achieved
for a wide constant range of λ values. Consequently, this new
approach has allowed us to extract the Doppler profile of the
endoclutter small boat target with a large separation from the
clutter background. This Doppler profile can be used for boat
detection and Doppler profile classification.
V. D ISCUSSION AND C ONCLUSION
We proposed a technique to separate the clutter from the
target in the endoclutter region using the MCA framework.
For maritime ISAR imaging, the technique was compared
with traditional range-Doppler processing for a boat, and for
a boat in a single range-cell, the SCR improvement was
calculated before and after the application of MCA. The key
contributions of this letter can be summarized as follows: 1) a
method to extract maritime targets in the endoclutter region
using MCA; 2) the first—as far as we are aware—application
of MCA for ISAR image formation; 3) the first—as far as
we are aware—application of MCA to small boat endoclutter Doppler extraction. The advantages of STFT dictionaries
relative to resonance-based dictionaries that were used in
[8] and [10] were also explained in the endoclutter region.
We also highlighted the fundamentally more intuitive approach
of improving SCR in nonstationary sea clutter relative to the
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