Open AccessArticle

Weak Target Detection Based on Full-Polarization Scattering Features under Sea Clutter Background

Yifei Fan

Duo Chen

^1,2,

Shichao Chen

^1,*,

Jia Su

¹,

Mingliang Tao

Zixun Guo

¹ and

Ling Wang

School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, China

Luoyang Institute of Electro-Optical Equipment, Aviation Industry of China, Luoyang 471000, China

Author to whom correspondence should be addressed.

Remote Sens. 2024, 16(16), 2987; https://doi.org/10.3390/rs16162987

Submission received: 22 May 2024 / Revised: 7 August 2024 / Accepted: 12 August 2024 / Published: 14 August 2024

(This article belongs to the Special Issue Technical Developments in Radar—Processing and Application)

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Abstract

Aiming at the low observable target detection under sea clutter backgrounds, this paper emphasizes the exploration of distinguishable full-polarization features between target and sea clutter echoes. To overcome the shortcomings of the existing polarization feature-based methods, the full-polarization features of sea clutter are modeled and analyzed in detail by using Van Zyl polarization decomposition. Then, three polarimetric features (the relative surface scattering energy, the relative dihedral scattering energy and the relative diffuse scattering energy) are extracted from the fully polarimetric radar sea clutter echoes, which improve the feature differences between sea clutter and targets. And a tri-polarimetric feature detector with constant false alarm rate (CFAR) is constructed based on the fast convex hull learning algorithm. The experimental results on the real measured IPIX radar datasets prove that the proposed full-polarization feature detector obtains more competitive detection performance and lower computational complexity than the several existing feature-based detectors.

Keywords:

sea clutter; low observable target; polarization decomposition; weak target detection

Graphical Abstract

1. Introduction

In the field of maritime detection, the electromagnetic echo from the ocean is named sea clutter, which is an unavoidable interference signal for target detection. The properties of sea clutter not only depend on radar working parameters but are also influenced by the marine environment. The traditional target detection methods mainly depend on the sea clutter amplitude distribution and intensity difference between targets and sea clutter [1,2,3,4,5,6,7]. For a high-resolution radar system, sea clutter exhibits non-uniform, non-stationary and non-Gaussian characteristics at a lower grazing angle condition. Moreover, sea clutter contains numerous spikes under higher states, which result in a significant increase in the false alarm rate (FAR). Therefore, the echoes of the low observable target with a smaller radar cross-section (RCS) and lower moving speed are faint and easily inundated by sea clutter. The conventional detectors (such as Moving Target detection and Coherent detection) are usually invalid for target detection in this condition. The reason is that the critical idea of those detection algorithms is subject to power competitions and Doppler differences between the target and sea clutter.

Feature-class detectors try to detect small targets by exploring deep levels of information from radar returns under sea clutter background. In the early 1990s, sea clutter was proven to possess fractal characteristics. In reference [8], the fractal dimension is utilized to detect the spherical buoy target. Xu et al. proposed a joint fractal detector [9], which extracts the Hurst exponent and the intercept at the optimal scale as a differential feature to achieve target detection. Then, several fractal-based target detection methods are proposed for weak target detection [10,11,12,13,14,15,16]. With further analysis of real sea clutter datasets, researchers developed other transform-domain feature detectors [17,18,19,20,21]. However, the feature-based target detectors only analyze the characteristic differences between sea clutter and targets from a certain perspective, which ignores the abundant information of the complex sea surface. Therefore, target detection methods under sea clutter background are advancing towards extracting multi-features from different fields [22,23,24]. Recently, Shui et al. put forward a tri-feature detector, which has a better detection performance than the joint fractal detector [25]. Shi et al. [26] analyze the differences between sea clutter and target echoes in graph connectivity, and several graph-based detectors are developed to improve the detection ability [27,28,29]. However, the feature-class detectors mentioned above achieve target detection only in the single-polarization channel, where multi-polarization information is not involved. Polarization diversity is a key tool to sensibly boost the detection performance of a radar system. In challenging situations, where angle and Doppler features of the radar returns cannot distinguish targets from background clutter, multi-polarimetric measurements provide valuable information for target detection [30]. In reference [31], Wang et al. firstly introduced polarization information of radar echoes into maritime target detection based on Cloud-Pottier decomposition and structured Distance between Entropy and Anisotropy (DBEA) as a feature for target detection. According to Freeman–Durden polarization decomposition, Xu et al. [32] designed a polarization feature detector and extracted polarization features from the polarization covariance matrix, which obtained a better detection performance than DBEA. However, the features extracted by the Freeman–Durden method may have a negative power phenomenon for real sea clutter data analysis, which leads to the decrease in the target detection performance.

To improve the polarization feature differences between sea clutter and weak targets, the Van Zyl decomposition is analyzed in detail for feature extraction in this paper, which utilizes eigenvalue decomposition to connect the electromagnetic scattering model of radar echoes. The non-coherent decomposition algorithm Van Zyl is a mixed decomposition model, which decomposes the average covariance matrix [33,34,35]. Hence, the feature extraction result of Van Zyl decomposition does not involve a negative power problem, while for small floating targets, the RCS of weak targets is too small to be detected using traditional CFAR-class and adaptive-class detectors [36,37,38]. Compared with the above-mentioned detectors, the convex hull learning algorithm utilizes clutter feature vectors to train the decision space, which avoids the problem of category non-equilibrium between clutter and target echoes effectively. Owing to the advantages of Van Zyl decomposition and the fast convex hull learning algorithm mentioned above, this paper proposes a novel polarization feature detector based on the fast convex hull learning algorithm. The feature vectors are formed by the relative surface scattering energy (

P_{r s}

), the relative dihedral scattering energy (

P_{r d}

) and the relative diffuse scattering energy (

P_{r f}

). The experimental results based on several real radar sea clutter datasets prove the preferable detection effect of the constructed polarization feature detector.

The remaining parts of this paper are as follows. In Part II, a concise introduction of the target detection model and the three polarization features is given in detail. Moreover, the target detector is constructed. The results of the three polarization features and target detection performance of real sea clutter datasets are analyzed in Part III. At last, the conclusion and expectation are summarized in Part IV.

2. Target Detection Model Analysis and Design of Polarization Feature Detector

2.1. Target Detection Model Analysis

For a specific range bin of the radar sea cutter datasets, the discrete echo series

y = [y (1), y (2), \dots, y (N)]

are segmented into

K

subsequences as follows:

y_{k} = y (m (k - 1) + 1, m (k - 1) + 2, \dots, m (k - 1) + L), k = 1, 2, \dots, K

(1)

where

m

represents the length of sliding window and

L

is the pulse numbers of each subsequence.

The model of the detection problem is commonly formulized as following binary hypothesis testing.

\{\begin{array}{l} H_{0} : \{\begin{array}{l} y_{k, J} = c_{k, J}, J = H H, H V, V H, V V \\ y_{k, J}^{p} = c_{k, J}^{p}, p = 1, 2 \dots, P \end{array} \\ H_{1} : \{\begin{array}{l} y_{k, J} = s_{k, J} + c_{k, J}, J = H H, H V, V H, V V \\ y_{k, J}^{p} = c_{k, J}^{p}, p = 1, 2 \dots, P \end{array} \end{array}

(2)

where hypothesis

H_{0}

indicates that there is no target in the subsequence under test (SUT), and the checking hypothesis

H_{1}

indicates that the SUT is a target subsequence.

y_{k, J}

s_{k, J}

and

c_{k, J}

represent the received echoes, target echoes and sea clutter echoes at the SUT from the J-th polarimetric channel.

P

represents the number of reference range bins, and

y_{k, J}^{p} = c_{k, J}^{p}

implies that the characteristics of sea clutter are similar both in reference cells and target cells.

2.2. Polarization Feature Extraction

It is known that electromagnetic scattering mechanisms between the sea surface and target have a distinct discrepancy, and the polarization properties of sea clutter are also different from the target echoes. For this reason, three polarization features are extracted to describe such differences and a feature-class detector is developed based on a fast convex hull learning algorithm.

Polarization target decomposition provides a substantive explanation for multi-polarization data, which have been widely applied in SAR signal processing. The present methods of polarization decomposition are divided into the following two classes. The first one is the coherent decomposition based on the polarization scattering matrix (PSM). The alternative class utilizes the non-coherent decomposition of the coherency matrix or covariance matrix. The Van Zyl decomposition belongs to the latter class, which is a hybrid of model-based decomposition and eigenvalue analysis. In fact, the Van Zyl decomposition takes eigenvalues of the average covariance matrix to link the physical scattering model and attempts to seek reasonable description for target characteristics. Based on the above discussion, it is seen that there are no negative power components of Van Zyl decomposition, which is suitably applied to maritime target detection. Therefore, the Van Zyl decomposition is adopted to extract distinguishable features and the detailed processes are shown as follows.

The first step is to construct PSM, which contains the scattering information of echoes. After choosing data from multi-polarization channels, PSM is formulated as

S = [\begin{matrix} S_{H H} & S_{H V} \\ S_{V H} & S_{V V} \end{matrix}]

(3)

where

S_{H H}

S_{H V}

S_{V H}

and

S_{V V}

represent radar echoes from

H H

H V

V H

and

V V

polarimetric channels, respectively. The Lexicographic basis is used to construct the orthogonal matrix, and the corresponding polarization scattering vector

Ω_{4 L}

is constructed as

Ω_{4 L} = {[\begin{matrix} S_{H H} & S_{H V} & S_{V H} & S_{V V} \end{matrix}]}^{T}

(4)

where

T

represents transpose. The PSM is obliquely symmetric by the reciprocity theorem, i.e.,

S_{H V} = S_{V H}

. The scattering vector

Ω_{4 L}

in (4) is degraded to

Ω_{3 L}

Then, the three-dimensional Lexicographic vector is constructed as

Ω_{3 L} = {[\begin{matrix} S_{H H} & \sqrt{2} S_{H V} & S_{V V} \end{matrix}]}^{T}

(5)

According to the Lexicographic vector

Ω_{3 L}

, the average covariance matrix

C

for a single base radar can be defined as

\begin{array}{l} C & = 〈Ω_{3 L} \otimes Ω_{3 L}^{H}〉 \\ = [\begin{matrix} 〈{|S_{H H}|}^{2}〉 & 0 & 〈S_{H H} S_{V V}^{*}〉 \\ 0 & 2 〈{|S_{H V}|}^{2}〉 & 0 \\ 〈S_{V V} S_{H H}^{*}〉 & 0 & 〈{|S_{V V}|}^{2}〉 \end{matrix}] \\ = c [\begin{matrix} 1 & 0 & ρ \\ 0 & η & 0 \\ ρ^{*} & 0 & ξ \end{matrix}] \end{array}

(6)

where

Ω_{3 L}^{H}

denotes the conjugate transpose of

Ω_{3 L}

, and

\otimes

denotes the Kronecker product of a matrix.

*

represents the conjugate, and

〈\cdot〉

represents the statistical average. The properties of symbols

c

η

ξ

and

ρ

depend on size, shape, electrical property and statistical angular distribution of scatterer respectively, which are defined as

\{\begin{array}{l} c = 〈{|S_{H H}|}^{2}〉, ρ = 〈S_{H H} S_{V V}^{*}〉 / 〈{|S_{H H}|}^{2}〉 \\ η = 2 〈{|S_{H V}|}^{2}〉 / 〈{|S_{H H}|}^{2}〉, ζ = 〈{|S_{V V}|}^{2}〉 / 〈{|S_{H H}|}^{2}〉 \end{array}

(7)

To ensure the non-singularity of C, the number of pulses

l e n

to construct C is required to be larger than 3. Equation (7) is substituted into (6), and the eigenvalues of the average covariance matrix

C

is calculated as

\{\begin{array}{l} λ_{1} = \frac{c}{2} (ζ + 1 + \sqrt{{(ζ - 1)}^{2} + 4 {|ρ|}^{2}}) \\ λ_{2} = \frac{c}{2} (ζ + 1 - \sqrt{{(ζ - 1)}^{2} + 4 {|ρ|}^{2}}) \\ λ_{3} = c η \end{array}

(8)

The corresponding eigenvectors

k_{1}

k_{2}

and

k_{3}

of the eigenvalues

λ_{1}

λ_{2}

and

λ_{3}

are also expressed as

\{\begin{array}{l} k_{1} = \sqrt{\frac{ζ - 1 + \sqrt{Δ}}{{|ζ - 1 + \sqrt{Δ}|}^{2} + 4 {|ρ|}^{2}}} {(2 ρ / (ζ - 1 + \sqrt{Δ}), 0, 1)}^{T} \\ k_{2} = \sqrt{\frac{ζ - 1 - \sqrt{Δ}}{{|ζ - 1 - \sqrt{Δ}|}^{2} + 4 {|ρ|}^{2}}} {(2 ρ / (ζ - 1 - \sqrt{Δ}), 0, 1)}^{T} \\ k_{3} = {(0, 1, 0)}^{T} \end{array}

(9)

where

Δ = {(ζ - 1)}^{2} + 4 {|ρ|}^{2} \geq 0

. By analyzing the forms of the above eigenvectors, it is found that the eigenvalues

λ_{1}

and

λ_{2}

are associated with surface scattering and dihedral scattering, respectively, and

λ_{3}

corresponds to diffuse scattering. For the convenience of simplification, several parameters are defined as

\{\begin{array}{l} Λ_{1} = λ_{1} [{(ζ - 1 + \sqrt{Δ})}^{2} / ({(ζ - 1 + \sqrt{Δ})}^{2} + 4 {|ρ|}^{2})] \\ Λ_{2} = λ_{2} [{(ζ - 1 + \sqrt{Δ})}^{2} / ({(ζ - 1 + \sqrt{Δ})}^{2} + 4 {|ρ|}^{2})] \\ Λ_{3} = λ_{3} \end{array}

(10)

α = \frac{2 ρ}{ζ - 1 + \sqrt{Δ}}, β = \frac{2 ρ}{ζ - 1 - \sqrt{Δ}}

(11)

According to the above analysis, the Van Zyl decomposition of the average covariance matrix

C

is expressed as

\begin{array}{l} C & = λ_{1} k_{1} k_{1}^{H} + λ_{2} k_{2} k_{2}^{H} + λ_{3} k_{3} k_{3}^{H} \\ = Λ_{1} [\begin{matrix} {|α|}^{2} & 0 & α \\ 0 & 0 & 0 \\ α^{*} & 0 & 1 \end{matrix}] + Λ_{2} [\begin{matrix} {|β|}^{2} & 0 & β \\ 0 & 0 & 0 \\ β^{*} & 0 & 1 \end{matrix}] + Λ_{3} [\begin{matrix} 0 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \end{matrix}] \end{array}

(12)

Once these parameters in Formula (11) are determined, the power of each scattering component can be calculated from (13).

\{\begin{array}{l} P_{s} = Λ_{1} (1 + {|α|}^{2}) \\ P_{d} = Λ_{2} (1 + {|β|}^{2}) \\ P_{f} = Λ_{3} \end{array}

(13)

where

P_{s}

P_{d}

and

P_{f}

represent surface scattering energy, dihedral scattering energy and diffuse scattering energy, respectively.

The

L / l e n

sets of polarization decomposition results are obtained from the four-polarization channel subsequence

x_{k, J}

of length L. The power summations of the odd scattering, even scattering and diffuse scattering are treated as features to distinguish targets from sea clutter in a statistical sense. The mathematical definition of these features is as follows.

P_{s} = \sum p_{s}, P_{d} = \sum p_{d}, P_{f} = \sum p_{f}

(14)

In the practical detection scenario, to overcome the power fluctuation and further improve the distinguishability of features, the relative values of the scattering energies between the bins under test and the reference bins are considered. Therefore, the relative surface scattering energy (

P_{r s}

), the relative dihedral scattering energy (

P_{r d}

) and the relative diffuse scattering energy (

P_{r f}

) are defined as

\{\begin{matrix} P_{r s} = \frac{P_{s}}{1 / K \sum_{k = 1}^{K} P_{s, q}} \\ P_{r d} = \frac{P_{d}}{1 / K \sum_{k = 1}^{K} P_{d, q}} \\ P_{r f} = \frac{P_{v}}{1 / K \sum_{k = 1}^{K} P_{f, q}} \end{matrix}

(15)

where

P_{s, q}

P_{d, q}

and

P_{f, q}

represent the surface scattering energy, dihedral scattering energy and diffuse scattering energy from the q-th reference range bin, respectively.

2.3. Feature-Based Detector

Due to the problem of category imbalance between target features and clutter features, the feature detection problem is transformed to anomaly detection, which only uses the pure clutter data to train the decision space.

In the practical detection problem, there are plenty of collected pure sea clutter fragments

c_{k, J}^{p} = [c_{k, H H}^{p}, c_{k, H V}^{p}, c_{k, V H}^{p}, c_{k, V V}^{p}], p = 1, 2 \dots, P

, and all the clutter feature vectors

\{η_{g}, g = 1, 2, \dots, P * K\}

are calculated by Formula (16). The conditional probability density functions

P (η_{g} | H_{0})

and

P (η_{g} | H_{1})

of the 3-D polarization feature vector

η

under the zero hypothesis

H_{0}

and alternative hypothesis

H_{1}

are presumed to be known. According to the Neyman–Pearson criterion, the optimal decision area of the detector is equivalent to the judgment space under the

H_{0}

hypothesis, which is defined as

\begin{array}{l} \max_{Ω} \{P_{d} = 1 - ∭_{Ω} P (η_{g} | H_{1}) d η_{g}\} \\ s . t ., ∭_{Ω} P (η_{g} | H_{0}) d η_{g} \geq 1 - P_{f}, \end{array}

(16)

where

P_{f}

represents the set false alarm probability, and

P_{d}

represents the detection probability. Nevertheless, there is a variety of targets in real detection environments, and the distribution of echoes from different targets in the feature space varies tremendously.

P (η_{g} | H_{1})

under the

H_{1}

hypothesis is unpredictable. Therefore, the optimal detection problem is simplified as

\begin{array}{l} \min_{Ω} \{|Ω|\} \\ s . t ., ∭_{Ω} P (η_{g} | H_{0}) d η_{g} = 1 - P_{f}, \end{array}

(17)

The decision space Ω is equated to the region contained in a bounded convex set to access the decision space and achieve the target detection efficiently. Then, the fast convex hull learning algorithm is adopted to obtain decision space with a certain FAR based on pure clutter feature vectors. The process can be formulated as

\{\begin{cases} \min_{Ω} \{V o l u m e (Θ)\}, \\ s . t . \frac{# \{l : η_{g} \in Θ\}}{G} = 1 - P_{f} \end{cases}

(18)

where

G

represents the number of clutter vectors,

\min \{\cdot\}

represents the minimum operator and

Θ

is the convex hull constructed by clutter vectors, which is denoted as

Θ \equiv S P \{a_{i}^{(1)}, a_{i}^{(2)}, a_{i}^{(3)}, i = 1, 2, \dots, I\}

(19)

where

a_{q}^{(1)}

a_{q}^{(2)}

and

a_{q}^{(3)}

denote the three vertices of the q-th triangular surface in the optimal judgment convex hull, respectively.

The training and detecting branches compose the basic framework of the proposed detector, which is displayed in Figure 1. The training branch includes clutter data collection, polarization feature extraction and decision space training. The detection branch consists of echoes acquisition, feature vector construction and judgment. The specific procedures of target detection are summarized as follows.

(1) Acquire radar scattering echoes and segment them into subsequences as SUTs.

(2) Extract polarization feature vector

η

from SUT.

(3) Calculate the value of test statistic

ς

ς \equiv \max \{|[a_{i}^{(1)} - η, a_{i}^{(2)} - η, a_{i}^{(3)} - η]|, i = 1, 2, \dots, I\}

(20)

where

I

denotes the number of triangular surfaces, which are the basic units of the convex hull.

(4) If

ς \leq 0

, it means that the feature vector

η

falls into the decision space and

H_{0}

stands; otherwise, feature vector

η

locates outside the decision space and

H_{1}

stands.

3. Experimental Results Analysis and Performance Evaluation

3.1. Real Measured IPIX Datasets

In the current work, the measured data applied are described as follows. Ten groups of sea surface datasets measured by McMaster University with an IPIX Radar in 1993 are adopted [39]. The IPIX Radar is a fully coherent X-band radar, which works at 9.3 GHz frequency. Among ten datasets, the sea conditions of #17 and #280 are approximately level 3–4, while the others are collected at level 2–3. All the datasets are collected at a low grazing angle condition. Each dataset includes multi-polarization channels such as HH, HV, VH and VV. Every dataset contains fourteen successive range bins, and any bin includes the pulse sequences of length

2^{17}

. The more detailed information about the radar parameters and environmental parameters are listed in Table 1, and the range-time-intensity image of the measured IPIX dataset #IPIX_26 is shown in Figure 2, respectively, which contains HH, HV, VH and VH polarization data.

To assess the performance of the proposed detector under various conditions, all the ten datasets in the four polarization modes are applied to analyze the detection performance between the proposed detectors and other existing detectors.

According to the above-mentioned datasets, the average signal-to-clutter ratios (average SCR) are mainly concentrated in 0–18 dB, which is affected by factors such as sea states and the radar-illuminated area of the target. It is worth noting that the average SCRs exhibit significant differences across the four polarization modes even within the same dataset. The specific values of the ten datasets are shown in Figure 3. The fluctuation of the target on the sea surface varies in different datasets and polarization conditions. Specifically, in the HH-polarized data of #30, the target is submerged in the heavy sea clutter, which leads to major differences in the average SCR.

3.2. Polarization Feature Analysis

According to the polarization feature extraction algorithm discussed before, the relative surface scattering energy (

P_{r s}

), the relative dihedral scattering energy (

P_{r d}

) and the relative diffuse scattering energy (

P_{r f}

) of the IPIX 54# datasets are calculated between sea clutter range bins and target range bins, where the feature statistical histogram results with L = 512, 2048 and 4096 are shown in Figure 4, Figure 5 and Figure 6.

From the results in Figure 4, Figure 5 and Figure 6, it is shown that the three features of the sea clutter range bins are distributed close to 0, while the three feature results of the target bins have a wider range value and long tail characteristic, whose values are larger than those of the sea clutter range bins. With the increase in the pulse numbers L, the feature distribution of range bins within the target becomes more dispersed. The feature distribution difference between sea clutter range bins and target range bins becomes more obvious. Meanwhile, the distribution of single-polarization features remains to exhibit different levels of overlapping, which fails to meet the demand for reliable detection.

To utilize the advantages of the three polarization features, the three-dimensional (3-D) polarization feature points

η = {[\begin{matrix} P_{r s} & P_{r d} & P_{r f} \end{matrix}]}^{T}

are constructed for target detection, where the x, y, z axis represents the three features

P_{r s}

P_{r d}

and

P_{r f}

, respectively. Then, the three-dimensional (3-D) polarization feature points

η = {[\begin{matrix} P_{r s} & P_{r d} & P_{r f} \end{matrix}]}^{T}

of the target bins and the pure clutter bins are calculated based on real sea clutter datasets, where the length of subsequence

L

is set as 512, 1024, 2048 and 4096. The above 3-D feature results are plotted in Figure 7. From Figure 7, it is seen that the polarization feature points of the target bins and the pure clutter bins are scattered in different regions. Moreover, as the length of subsequence

L

increases, the feature points of the same class become more gathered and the gap between different classes becomes more obvious, which means that the 3-D polarization features have potential abilities for target detection from sea clutter backgrounds.

Figure 8a shows the 3-D features of the sea clutter series vector of the # 54 dataset, and Figure 8b shows the decision convex hull constructed by pure clutter with an FAR of 1‰ in 3-D space. Then, the target detection performance is analyzed in the next section.

3.3. Detection Performance Analysis

In this part, the performance of the proposed detector is assessed by the above-mentioned datasets. In the first experiment, the FAR is set to be 1‰, and the length of subsequence

L

is set as 512, 1024, 2048 and 4096, respectively. The length of the sliding window is set as 64. Figure 9 shows the detection results of the recently effective polarization feature detectors: the DBEA detector [31], tri-polarization feature detector [32] and the proposed detector. It is seen from Figure 9 that the proposed detector attains more competitive probability than the existing polarization detectors. Firstly, the proposed detector and the tri-polarization feature detector both provide an improved performance compared to the DBEA detector as the complementary multi-dimensional polarization features more adequately portray the difference between sea clutter and targets. As shown in Figure 9a, the average detection probability of the proposed detector is 5% greater than the detector in [32] under the conditions of low SCR and short observation time. The Van Zyl decomposition solves the negative power problem in [32], and the extracted features on this basis show a more distinctive distribution in the polarization feature space.

In the second experiment, the average receiver operating characteristic (ROC) curves of all the above-mentioned datasets for the joint-fractal detector [14], tri-feature detector [25], the graph feature detector [26], DBEA detector [31], tri-polarization feature detector [32] and the proposed detector are compared in Figure 10. The length of subsequence

L

is set as 4096. The FAR ranges from 0.001 to 0.1 to observe the classification ability of each detector under different false alarm conditions.

From Figure 10a, it is found that the proposed detector attains preferable performance to the two comparisons of existing polarization detectors under a different false alarm rate. The Van Zyl decomposition combines model decomposition and eigenvalue analysis, and the proposed detector on this basis effectively avoids the negative power problem and improves the detection performance under different false alarm conditions. In Figure 10b–d, the average ROC curves of effective feature detectors are compared with the proposed method. It is seen that the proposed detector maintains an effective detection ability at lower false alarm conditions over the detectors in the single-polarization channel.

Additionally, the computational complexity of extracting the tri-polarization features

P_{r s}

P_{r d}

and

P_{r f}

is only

O (4 L)

, which means that extracting polarization features is faster than the joint-fractal-based detector [14] and tri-feature detector [25]. Table 2 contrasts the time costs for feature extraction of those detectors from a dataset and confirms the point.

4. Conclusions

This paper mainly focuses on low observable target detection under sea clutter background. To overcome the shortcomings of the existing feature-based detection methods, the Van Zyl decomposition is utilized to extract three novel polarimetric features, which are adopted to construct a 3-D feature detector to identify low observable targets under sea clutter backgrounds. Compared with the existing polarimetric feature detector, joint-fractal feature detector and original tri-feature detector, the proposed detector obtains a preferable detection performance for low observable targets. The main contributions of the proposed algorithm can be summarized as follows:

(1) Rather than the traditional single-polarization feature-based detection method, this paper takes full advantage of the multi-polarization features of sea clutter, which can increase the differences between sea clutter and targets.

(2) The Van Zyl decomposition is taken for feature extraction in this paper, which utilizes eigenvalue decomposition to connect the electromagnetic scattering model of radar echoes. The non-coherent Van Zyl decomposition algorithm is a mixed decomposition model, which solves the negative power problem in [32]. The extracted features on this basis show a more distinctive distribution in the polarization feature space.

(3) Rather than a traditional CFAR detector, the convex hull learning algorithm utilizes clutter feature vectors to train the decision space, which avoids the problem of category non-equilibrium between clutter and target echoes effectively.

(4) Compared to the existing feature-based detection methods, the proposed polarization feature extraction requires lower computational complexity, and the proposed detector runs more efficiently.

In the future, the proposed polarization features can be developed as components of higher-dimensional detectors to obtain preferable target detection performance.

Author Contributions

Y.F. came up with the idea and designed the experiments. D.C. implemented the experiment, obtained the results and drafted the manuscript. S.C., M.T., Z.G. and J.S. contributed to discuss the idea and results. L.W. contributed to revising the manuscript. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported in part by the National Natural Science Foundation of China under Grant 62171379. This work is also partly funded by the Shanghai Aerospace Science and Technology Innovation Fund under grant SAST2023-044.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors on request.

Conflicts of Interest

Author Duo Chen was employed by the company Luoyang Institute of Electro-Optical Equipment, Aviation Industry of China. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

References

Carretero-Moya, J.; Gismero-Menoyo, J.; Blanco-del-Campo, Á.; Asensio-Lopez, A. Statistical Analysis of a High-Resolution Sea-Clutter Database. IEEE Trans. Geosci. Remote Sens. 2010, 48, 2024–2037. [Google Scholar] [CrossRef]
Fiche, A.; Angelliaume, S.; Rosenberg, L.; Khenchaf, A. Analysis of X-band SAR sea-clutter distributions at different grazing angles. IEEE Trans. Geosci. Remote Sens. 2015, 53, 4650–4660. [Google Scholar] [CrossRef]
Xin, Z.; Liao, G.; Yang, Z.; Zhang, Z.; Dang, H. Analysis of Distribution Using Graphical Goodness of Fit for Airborne SAR Sea-Clutter Data. IEEE Trans. Geosci. Remote Sens. 2017, 55, 5719–5728. [Google Scholar] [CrossRef]
Rosenberg, L.; Bocquet, S. Application of the Pareto plus noise distribution to medium grazing angle sea-clutter. IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens. 2015, 8, 255–261. [Google Scholar] [CrossRef]
Mezache, A.; Soltani, F.; Sahed, M.; Chalabi, I. Model for non-Rayleigh clutter amplitudes using compound inverse Gaussian distribution: An experimental analysis. IEEE Trans. Aerosp. Electron. Syst. 2015, 51, 143–153. [Google Scholar] [CrossRef]
Conte, E.; De Maio, A.; Galdi, C. Statistical analysis of real clutter at different range resolutions. IEEE Trans. Aerosp. Electron. Syst. 2004, 40, 903–918. [Google Scholar] [CrossRef]
Sahed, M.; Kenane, E.; Khalfa, A. Exact Closed-Form Pfa Expressions for CA-CFAR and GO-CFAR Detectors in Gamma-Distributed Radar Clutter. IEEE Trans. Aerosp. Electron. Syst. 2023, 59, 4674–4679. [Google Scholar] [CrossRef]
Lo, T.; Leung, H.; Litva, J.; Haykin, S. Fractal characterisation of sea-scattered signals and detection of sea-surface targets. IEEE Proc. F-Radar Signal Process. 1993, 140, 243–250. [Google Scholar] [CrossRef]
Xu, X. Low observable targets detection by joint fractal properties of sea clutter: An experimental study of IPIX OHGR datasets. IEEE Trans. Antennas Propag. 2010, 58, 1425–1429. [Google Scholar]
Fan, Y.; Tao, M.; Su, J.; Wang, L. Weak target detection based on joint fractal characteristics of autoregressive spectrum in sea clutter background. IEEE Trans. Geosci. Remote Sens. 2019, 16, 1070–1077. [Google Scholar] [CrossRef]
Xiong, G.; Xi, C.; Dong, D.; Yu, W. Cross correlation singularity power spectrum theory and application in radar target detection within sea clutter. IEEE Trans. Geosci. Remote Sens. 2019, 57, 3753–3765. [Google Scholar] [CrossRef]
Fan, Y.; Tao, M.; Su, J.; Wang, L. Weak target detection based on whole-scale Hurst exponent of autoregressive spectrum in sea clutter background. Digit. Signal Process. 2020, 101, 102714. [Google Scholar] [CrossRef]
Fan, Y.; Luo, F.; Li, M. Weak target detection in sea clutter background using local-multifractal spectrum with adaptive window length. IET Radar Sonar Navig. 2015, 9, 835–842. [Google Scholar] [CrossRef]
Hu, J.; Tung, W.; Gao, J. Detection of low observable targets within sea clutter by structure function based multifractal analysis. IEEE Trans. Antennas Propag. 2006, 54, 136–143. [Google Scholar] [CrossRef]
Guo, Z.; Shui, P.; Bai, X. Small target detection in sea clutter using all-dimensional Hurst exponents of complex time sequence. Digit. Signal Process. 2020, 101, 102707. [Google Scholar] [CrossRef]
Fan, Y.; Tao, M.; Su, J. Multifractal Correlation Analysis of Autoregressive Spectrum-Based Feature Learning for Target Detection Within Sea Clutter. IEEE Trans. Geosci. Remote Sens. 2021, 60, 1–11. [Google Scholar] [CrossRef]
Shi, S.; Shui, P. Sea-surface floating small target detection by one-class classifier in time-frequency feature space. IEEE Geosci. Remote Sens. Lett. 2018, 56, 6395–6411. [Google Scholar] [CrossRef]
Xie, J.; Xu, X. Phase-Feature-Based Detection of Small Targets in Sea Clutter. IEEE Geosci. Remote Sens. Lett. 2022, 19, 1–5. [Google Scholar] [CrossRef]
Yu, X.; Chen, X.; Huang, Y. Radar Moving Target Detection in Clutter Background via Adaptive Dual-Threshold Sparse Fourier Transform. IEEE Access 2019, 7, 58200–58211. [Google Scholar] [CrossRef]
Guo, Z.; Shui, P.; Bai, X. Sea-Surface small target detection based on K-NN with controlled false alarm rate in sea clutter. J. Radars 2020, 9, 654–663. [Google Scholar]
Shi, Y.; Chen, W. Sea Surface Target Detection Using Global False Alarm Controllable Adaptive Boosting Based on Correlation Features. IEEE Trans. Geosci. Remote Sens. 2023, 61, 1–14. [Google Scholar] [CrossRef]
Zhou, H.; Jiang, T. Decision tree based sea-surface weak target detection with false alarm rate controllable. IEEE Signal. Process. Lett. 2019, 26, 793–797. [Google Scholar] [CrossRef]
Guo, Z.; Shui, P. Anomaly Based Sea-Surface Small Target Detection Using K-Nearest Neighbor Classification. IEEE Trans. Aerosp. Electron. Syst. 2020, 56, 4947–4964. [Google Scholar] [CrossRef]
Guo, Z.; Bai, X.; Li, J.; Shui, P. Fast Detection of Small Targets in High-Resolution Maritime Radars by Feature Normalization and Fusion. IEEE J. Ocean. Eng. 2022, 47, 736–750. [Google Scholar] [CrossRef]
Shui, P.; Li, D.; Xu, S. Tri-feature-based detection of floating small targets in sea clutter. IEEE Trans. Aerosp. Electron. Syst. 2014, 50, 1416–1430. [Google Scholar] [CrossRef]
Shi, Y.; Yao, T.; Guo, Y. Floating Small Target Detection Based on Graph Connected Density in Sea Surface. J. Electron. Inf. Technol. 2021, 43, 3185–3192. [Google Scholar]
Su, N.; Chen, X.; Guan, J.; Huang, Y.; Wang, X.; Xue, Y. Radar Maritime Target Detection via Spatial–Temporal Feature Attention Graph Convolutional Network. IEEE Trans. Geosci. Remote Sens. 2024, 62, 1–15. [Google Scholar] [CrossRef]
Su, N.; Chen, X.; Guan, J.; Huang, Y. Maritime Target Detection Based on Radar Graph Data and Graph Convolutional Network. IEEE Geosci. Remote Sens. Lett. 2022, 19, 1–5. [Google Scholar] [CrossRef]
Xu, S.; Jiao, Y.; Bai, X.; Jiang, J. Small Target Detection Based on Frequency Domain Multichannel Graph Feature Perception on Sea Surface. J. Electron. Inf. Technol. 2023, 45, 1567–1574. [Google Scholar]
Augusto, A.; Antonio, D.M.; Alfonso, F. Polarimetric Radar Signal Processing; SciTech Publishing Inc., Raleigh, NC, USA, 2022.
Wu, P.; Wang, J.; Wang, W. Small Target Detection in Sea Clutter Based on Polarization Characteristics Decomposition. J. Electron. Inf. Technol. 2011, 33, 816–822. [Google Scholar] [CrossRef]
Xu, S.; Zheng, J.; Pu, J.; Shui, P. Sea-surface floating small target detection based on polarization features. IEEE Geosci. Remote Sens. Lett. 2018, 15, 1505–1509. [Google Scholar] [CrossRef]
Van Zyl, J.J. Application of Cloude’s target decomposition theorem to polarimetric imaging radar data. Opt. Photonics 1993, 1748, 184–212. [Google Scholar]
Van Zyl, J.J.; Arii, M.; Kim, Y. Model-Based Decomposition of Polarimetric SAR Covariance Matrices Constrained for Nonnegative Eigenvalues. IEEE Geosci. Remote Sens. 2011, 49, 3452–3459. [Google Scholar] [CrossRef]
Zhao, Y.; He, W.; Ren, H. Polarization Descattering Imaging of Underwater Complex Targets Based on Mueller Matrix Decomposition. IEEE Photonics J. 2022, 14, 1–6. [Google Scholar]
Martín-de-Nicolás, J.; Jarabo-Amores, P.; Rey-Maestre, N.; Mata-Moya, D.; Bárcena-Humanes, J.L. A non-parametric CFAR detector based on SAR sea clutter statistical modelling. In Proceedings of the 2015 IEEE International Conference on Image Processing, Quebec City, QC, Canada, 27–30 September 2015; pp. 4426–4430. [Google Scholar]
Kuang, C.; Wang, C.; Wen, B. An Improved CA-CFAR Method for Ship Target Detection in Strong Clutter Using UHF Radar. IEEE Signal Process. Lett. 2020, 27, 1445–1449. [Google Scholar] [CrossRef]
Yang, H.; Zhang, T.; He, Y. GPU-Oriented Designs of Constant False Alarm Rate Detectors for Fast Target Detection in Radar Images. IEEE Trans. Geosci. Remote Sens. 2022, 60, 1–14. [Google Scholar] [CrossRef]
The IPIX Radar Database [EB/OL]. 2001. Available online: http://soma.ece.mcmaster.ca/ipix/ (accessed on 1 January 2001).

Figure 1. Flowchart of the proposed feature-based detector.

Figure 2. The range-time-intensity image of the sea clutter datasets. (a) #26 HH polarization. (b) #26 HV polarization. (c) #26 VH polarization. (d) #26 VV polarization.

Figure 3. The average SCRs of ten sets of datasets.

Figure 4. Polarization feature distributions of sea clutter range bins and target range bins (

L = 512

). (a) Prs distribution of sea clutter range bins. (b) Prs distribution of target range bins. (c) Prd distribution of sea clutter range bins. (d) Prd distribution of target range bins. (e) Prf distribution of sea clutter range bins. (f) Prf distribution of target range bins.

Figure 4. Polarization feature distributions of sea clutter range bins and target range bins (

L = 512

Figure 5. Polarization feature distributions of sea clutter range bins and target range bins (

L = 2048

Figure 5. Polarization feature distributions of sea clutter range bins and target range bins (

L = 2048

Figure 6. Polarization feature distributions of sea clutter range bins and target range bins (

L = 4096

Figure 6. Polarization feature distributions of sea clutter range bins and target range bins (

L = 4096

Figure 7. Distributions of feature points of target bins and pure clutter in 3-D space when the length of subsequence L is set as (a) L = 512, (b) L = 1024, (c) L = 2048, (d) L = 4096.

Figure 8. The decision convex hull with a false alarm of 1‰. (a) Distributions of clutter feature points in 3-D space, (b) decision convex hull constructed by clutter feature points.

Figure 9. Detection probabilities of the proposed detector, tri-polarization feature detector [32] and DBEA detector [31] for ten datasets when the length of subsequence

L

Figure 9. Detection probabilities of the proposed detector, tri-polarization feature detector [32] and DBEA detector [31] for ten datasets when the length of subsequence

L

Figure 10. Comparison average ROC curves. (a) The proposed detector and classical polarization detector, (b) the proposed detector and joint-fractal detector, (c) the proposed detector and tri-feature detector, (d) the proposed detector and graph connectivity detector.

Table 1. Dataset information.

Performance Indexes	Values	Dataset Labels	CUT	Guard Bins
Frequency	9.39 GHz	19931111163625starea54	8	7, 9, 10
PRF	1 KHz	19931109191449starea30	7	6, 8
Target	buoy	19931109202217starea30	7	6, 8, 9
Radar height	30 m	19931118162155starea310	7	6, 8, 9
Range	30 m	19931118162625starea311	7	6, 8, 9
resolution	30 m	19931118174259starea320	7	6, 8, 9
		19931110001635starea40	7	5, 6, 8
		19931108220902starea26	7	6, 8
		19931118023604starea280	8	7, 10
		19931107135603starea17	9	8, 10, 11

Table 2. Time cost contrast.

The Length of Subsequence	512	1024	2048	4096 s
The proposed detector	1.96 s	2.37 s	3.40 s	4.78 s
Joint-fractal-based detector [14]	3.58 s	4.82 s	7.44 s	14.66 s
Tri-feature detector [25]	3.59 s	5.74 s	9.00 s	15.68 s

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Fan, Y.; Chen, D.; Chen, S.; Su, J.; Tao, M.; Guo, Z.; Wang, L. Weak Target Detection Based on Full-Polarization Scattering Features under Sea Clutter Background. Remote Sens. 2024, 16, 2987. https://doi.org/10.3390/rs16162987

AMA Style

Fan Y, Chen D, Chen S, Su J, Tao M, Guo Z, Wang L. Weak Target Detection Based on Full-Polarization Scattering Features under Sea Clutter Background. Remote Sensing. 2024; 16(16):2987. https://doi.org/10.3390/rs16162987

Chicago/Turabian Style

Fan, Yifei, Duo Chen, Shichao Chen, Jia Su, Mingliang Tao, Zixun Guo, and Ling Wang. 2024. "Weak Target Detection Based on Full-Polarization Scattering Features under Sea Clutter Background" Remote Sensing 16, no. 16: 2987. https://doi.org/10.3390/rs16162987

APA Style

Fan, Y., Chen, D., Chen, S., Su, J., Tao, M., Guo, Z., & Wang, L. (2024). Weak Target Detection Based on Full-Polarization Scattering Features under Sea Clutter Background. Remote Sensing, 16(16), 2987. https://doi.org/10.3390/rs16162987

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Weak Target Detection Based on Full-Polarization Scattering Features under Sea Clutter Background

Abstract

1. Introduction

2. Target Detection Model Analysis and Design of Polarization Feature Detector

2.1. Target Detection Model Analysis

2.2. Polarization Feature Extraction

2.3. Feature-Based Detector

3. Experimental Results Analysis and Performance Evaluation

3.1. Real Measured IPIX Datasets

3.2. Polarization Feature Analysis

3.3. Detection Performance Analysis

4. Conclusions

Author Contributions

Funding

Data Availability Statement

Conflicts of Interest

References

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