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A Correlation-Based Joint CFAR Detector Using Adaptively-Truncated Statistics in SAR Imagery Jiaqiu Ai 1, *, Xuezhi Yang 1 , Fang Zhou 1 , Zhangyu Dong 1 , Lu Jia 1 and He Yan 2 1

2

*

School of Computer and Information, Hefei University of Technology, Tunxi Road, Hefei 230009, China; [email protected] (X.Y.); [email protected] (F.Z.); [email protected] (Z.D.); [email protected] (L.J.) College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Yudao Avenue, Nanjing 210016, China; [email protected] Correspondence: [email protected]; Tel.: +86-189-4984-7147

Academic Editor: Jonathan Li Received: 9 December 2016; Accepted: 21 March 2017; Published: 27 March 2017

Abstract: Traditional constant false alarm rate (CFAR) detectors only use the contrast information between ship targets and clutter, and they suffer probability of detection (PD) degradation in multiple target situations. This paper proposes a correlation-based joint CFAR detector using adaptively-truncated statistics (hereafter called TS-2DLNCFAR) in SAR images. The proposed joint CFAR detector exploits the gray intensity correlation characteristics by building a two-dimensional (2D) joint log-normal model as the joint distribution (JPDF) of the clutter, so joint CFAR detection is realized. Inspired by the CFAR detection methodology, we design an adaptive threshold-based clutter truncation method to eliminate the high-intensity outliers, such as interfering ship targets, side-lobes, and ghosts in the background window, whereas the real clutter samples are preserved to the largest degree. A 2D joint log-normal model is accurately built using the adaptively-truncated clutter through simple parameter estimation, so the joint CFAR detection performance is greatly improved. Compared with traditional CFAR detectors, the proposed TS-2DLNCFAR detector achieves a high PD and a low false alarm rate (FAR) in multiple target situations. The superiority of the proposed TS-2DLNCFAR detector is validated on the multi-look Envisat-ASAR and TerraSAR-X data. Keywords: SAR; ship detection; correlation-based joint CFAR; 2D joint log-normal distribution; adaptively truncated clutter statistics

1. Introduction Synthetic aperture radar (SAR) is an active radar that can provide high-resolution images in the microwave band under all weather conditions. SAR images are less influenced by the time and weather conditions than the optical images, therefore, they are more suitable for ship detection. Nowadays, SAR images have been widely used for fishing vessel detection, ship traffic monitoring and immigration control [1–6]. The well-known constant false alarm rate (CFAR) detectors adaptively calculate the detection threshold based on parameter estimation and precise modeling of the background clutter. The statistical model of the clutter is usually accomplished by local parameter estimation of a moving reference window which is divided into the test window, the guard window, and the background window. For the simplest case, when the test window only comprises one pixel, we only have to estimate the statistical distribution of the clutter. The statistical models have been extensively studied in the past decades, and quite a number of models, such as log-normal [7], Weibull [8], generalized Gamma [9], K [10], alpha-stable [11], and G model [12], etc., have been developed. CFAR detection is realized to compare the pixels in the test window with the local calculated threshold. The CFAR detectors Sensors 2017, 17, 686; doi:10.3390/s17040686

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based on K (K-CFAR), G, alpha-stable, and generalized Gamma, etc., suffer complex parameter estimation and heavy computational burden. However, cell-averaging CFAR (CA-CFAR) [13] and two-parameter CFAR (abbreviated as NM-CFAR in the intensity domain, and LN-CFAR in the log-intensity domain) [14] are widely used for simple parameter estimation and high computational efficiency. CA-CFAR uses negative exponential distribution for single-look images and gamma distribution for multi-look images. CA-CFAR only estimates the mean value, however, while NM-CFAR and LN-CFAR assume that the statistical distribution of the clutter is Gaussian, and they estimate two parameters (mean and standard deviation) in the intensity domain and the log-intensity domain, respectively. CA-CFAR has good performance in homogeneous state, and two parameter CFAR performs well in non-homogeneous state. When the test window encompasses multiple pixels (e.g., nine pixels for a 3 × 3 test window), we need to estimate the JPDF of the clutter, which is a much more complicated task. However, in SAR images, every pixel of the clutter is correlated with its neighborhood, and the same to the target. Thus, in the simplest way, we can exploit the correlation information between neighboring pixels and model their JPDF. The first author of this paper, Ai [15], built a 2D joint log-normal (2DLN) distribution to model the JPDF of the clutter and, thus, correlation-based joint CFAR detection (2DLN-CFAR) is realized. As for statistical modeling, the statistical models are established using the statistics estimated from the local background window. However, in practice, the clutter in the local background window is often contaminated by the high-intensity outliers such as interfering ship targets, side-lobes, and ghosts caused by the low pulse repetition frequency (PRF). The high-intensity outliers in the background window lead to parameter overestimation, which causes inaccurate statistical modeling. Consequently, the FAR drops, but the PD degrades, known as the capture effect. Numerous studies [16–44] have been carried out by means of extracting the clutter pixels in the background window and eliminating the influence of the high-intensity outliers. The order statistic CFAR (OS-CFAR) [16] is designed to overcome the above problem arisen in CA-CFAR. OS-CFAR has a significant advantage when detecting targets in multiple target situations, but the optimal statistic is obtained by experience and the computational efficiency is quite low. The smallest-of CFAR (SO-CFAR) [17] and the greatest-of CFAR (GO-CFAR) [18] choose the smallest and the largest mean value of the divided background windows as the local detection threshold. They both achieve improved detection performance in the background containing high-intensity outliers, but GO-CFAR suffers PD degradation and SO-CFAR suffers an increased FAR. The variability index CFAR (VI-CFAR) [19] dynamically selects a particular group of reference pixels for parameter estimation, and the test statistic is selected by a comprehensive method using CA-CFAR, SO-CFAR, and GO-CFAR. It performs well both in homogeneous and non-homogeneous backgrounds, but it suffers a detection loss in heterogeneous clutter. The trimmed mean CFAR [20] obtains the detection threshold using the mean value of the intensity ranked samples, but the optimum detection performance relies on the selection of the trimmed samples. The region classification CFAR (RC-CFAR) [21] subdivides the reference cell into four parts so that the number of target samples in each part becomes too small, thus, it is less credible to judge whether the background is non-homogeneous. The automatic censoring scheme [22–36] excludes the interfering outliers from the background clutter, so the statistical model is more accurate and the capture effect can be greatly alleviated. However, it is realized through additional iterative data censoring, which generally requires many cycles and long calculation time. Moreover, a method based on sub-aperture cross-correlation magnitude is proposed in [37], then the sub-band extraction strategy is further studied in [38]. However, sub-aperture processing in such methods degrades the spatial resolution and is unfavorable to detect small ships. A modified CFAR algorithm based on object proposals [39] uses an object proposal generator based on gradient features to generate a small set of object proposals. However, it spends much time on the object proposal generation, and the CFAR detection accuracy is affected by the object proposal procedure. Superpixel-based CFAR [40] incorporates the superpixel approach into the two-parameter CFAR detector. Superpixel approach-based segmentation is firstly implemented, and then two-parameter CFAR is applied on

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the segmented regions. Although it achieves a good result in multiple target situations, it suffers a heavy computational burden on the superpixel approach-based segmentation. In addition, there are many hybrid CFAR detectors designed to accommodate reversal clutter backgrounds in one algorithm. These CFAR detectors incorporate different strategies and dynamically choose the appropriate one. One classical example is the censored mean-level detector (CMLD) [41], which employs both data ranking and censoring methods to obtain improved performance in the presence of interfering targets. It excludes the largest reference sample and uses the remaining for parameter estimation. CMLD is quite robust in multiple-target situations, but it suffers some detection loss in homogeneous state. Moreover, without prior knowledge of the interfering targets, it may lose its robustness. The truncated statistics-based CFAR detector (TS-CFAR) [42,43] ranks the pixels in the background window based on gray intensity in a descending order. Then a truncation depth is set empirically (such as 25% in the experiments), and the high-intensity samples are discarded. Finally, the detection threshold is calculated using the remaining low-intensity samples. Furthermore, the same author of [43] proposed a segmentation-based CFAR detection algorithm using truncated statistics [44], segmentation is firstly implemented on the SAR images, and then truncated statistics-based CFAR is applied to the segmented regions. However, parameter estimation and threshold calculation in [42–44] need iterative numerical solutions, which are computationally ineffective. Moreover, the truncated statistics based CFAR detectors improve the PD, but the FAR rises because of the exclusion of the high-intensity clutter pixels from the background samples. Traditional CFAR detectors simply use the contrast information between ship targets and the clutter, but the gray intensity correlation information is ignored. Furthermore, in multiple target situations, improved CFAR detectors are designed to enhance the PD through clutter extraction. However, the clutter samples are acquired through iterative data censoring or clutter trimming, the former needs many cycles and long calculation time, and the latter suffers a high FAR because the clutter samples are incomplete. This paper proposes a correlation-based joint CFAR detector using adaptively-truncated clutter statistics in SAR imagery. Compared with traditional CFAR detectors, our main contribution is stated as follows: (1)

(2)

(3)

In addition to the contrast information between ship targets and the clutter, the proposed joint CFAR detector exploits the gray intensity correlation characteristics in the clutter and ship targets. Joint CFAR detection is realized by building a 2D joint log-normal model as the JPDF of the clutter. 2DLN-CFAR [15] only exploits the gray intensity correlation of the eight-neighborhood, this paper extends it to a wider neighborhood, and more correlation information can be used to further lower the FAR, while the PD is obtained at a high level. In multiple target situations, 2DLN-CFAR and traditional CFAR detectors suffer PD degradation. Inspired by the CFAR detection methodology, the proposed CFAR detector designs an adaptive threshold-based clutter truncation method to eliminate the high-intensity outliers from the clutter samples in the background window, and the real clutter is preserved to the largest degree. The threshold is adaptively calculated by comprehensive consideration of real clutter preservation and high-intensity outlier elimination. A 2D joint log-normal model is accurately built using the adaptively-truncated clutter by simple parameter estimation, so the PD of the joint CFAR detector is greatly improved. The proposed TS-2DLNCFAR detector achieves a high PD and a low FAR, which can greatly eliminate the capture effect in multiple target situations.

The rest of the paper is organized as follows: In Section 2, the correlation-based joint CFAR detection methodology is introduced. In Section 3, the proposed TS-2DLNCFAR detector is detailed. In Section 4, experimental results are given with detailed analysis. Finally, Section 5 concludes this paper.

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2. Correlation-Based Joint CFAR Detection In SAR images, the gray intensity of ship targets is larger than that of the clutter because of the strong backscattering cross-section of the dihedral, trihedral, and polyhedral corner reflectors. Furthermore, every pixel’s gray intensity is correlated with its neighborhood. The first author of this paper, Ai [15], comprehensively used the contrast and the correlation information, and 2DLN distribution was built to model the JPDF of the clutter to realize joint CFAR detection. 2DLN model of the JPDF is defined as [15]:   (ln( X )−µln )2 −2rθ (ln( X )−µln )(ln(Y )−µln )+(ln(Y )−µln )2 1 √ √ f ( X, Y, θ ) = exp − (1) 2 2 2 2 2πσln

1−rθ XY

2

1−rθ σln

where µln and σln are the mean and standard deviation of the local background window in the log-intensity domain. X and Y are the gray intensity of a pixel and its neighborhood in the direction of θ [15] uses a test window with a size of 3 × 3 pixels, and the gray intensity correlation in the four directions (horizontal, vertical, diagonal and anti-diagonal) are comprehensively used. rθ is the spatial correlation coefficient used for correlation evaluation, which is defined as [45]: M N

∑ ∑ [ f (i, j) − µ][ f (i + l, j + k) − µ]

rθ (l, k ) =

i =1 j =1

,

M N

(2)

2 ∑ ∑ [ f (i, j) − µ]

i =1 j =1

where µ is the mean value of the SAR image in the intensity domain, f (i, j) is the intensity value of the pixel located at (i, j), f (i + l, j + k )is the intensity value of its neighboring pixel located at (i + l, j + k ). l and k are the distance values in the horizontal and vertical direction. (1) horizontal: l = 0, k = 1; (2) vertical: l = 1, k = 0; (3) diagonal: l = −1, k = 1; and (4) anti-diagonal: l = 1, k = 1. 2D joint CFAR detection can be realized using the joint CFAR detection threshold T calculated from the probability of false alarm (PFA) PFA by: PFA =

Z ∞ T

dy

Z ∞ T

f ( X, Y, θ )dx

(3)

2D joint CFAR detection results in the four directions are acquired as follows: Horizontal : if f (i, j) > TH and f (i, j + 1) > TH , f dH (i, j) = 1 and f dH (i, j + 1) = 1, Vertical : if f (i, j) > TV and f (i + 1, j) > TV , f dV (i, j) = 1 and f dV (i + 1, j) = 1, Diagonal : if f (i, j) > TD and f (i − 1, j + 1) > TD , f dD (i, j) = 1 and f dD (i − 1, j + 1) = 1,

(4)

Anti − diagonal : if f (i, j) > TA and f (i + 1, j + 1) > TA , f dA (i, j) = 1 and f dA (i + 1, j + 1) = 1,

where TH , TV , TD and TA are the joint CFAR detection thresholds in the horizontal, vertical, diagonal, and anti-diagonal direction, and f dH , f dV , f dD and f dA are the joint CFAR detection results in the horizontal, vertical, diagonal, and anti-diagonal directions. The points labeled as “1” are regarded as ship targets. The final joint CFAR detection result is obtained by fusing the four detection results with the “OR” operation [15]. 2DLN-CFAR [15] only uses the correlation information of the eight-neighborhood. However, in SAR images, ship targets are presented as a cluster of bright pixels with a certain length and width. In addition to the eight-neighborhood, we can exploit more correlation information in a wider neighborhood. Suppose the test window is 7 × 7 pixels, we can obtain the joint CFAR detection results with neighboring distances of 1, 2, and 3 pixels, as shown in Figure 1. We only use the correlation information in the horizontal, vertical, diagonal, and anti-diagonal directions instead of all directions to reduce the redundancy and improve the computational efficiency. The gray intensity of neighboring pixels with a certain distance are compared with the joint CFAR detection threshold calculated through Equation (3), and the joint CFAR detection results are acquired by Equation (4).

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



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(a) (b) Figure 1. Different distances usedfor for joint CFAR detection 7 ×window: 7 test window: Figure 1. Differentneighboring neighboring distances used joint CFAR detection withwith a(c)7 × a7 test (a) (a) one (b)two twopixels; pixels;and and three pixels. one pixel; pixel; (b) (c)(c) three pixels. Figure 1. Different neighboring distances used for joint CFAR detection with a 7 × 7 test window: (a) one pixel; (b) twodetection pixels; andresult (c) three joint CFAR ofaapixels. certain direction information of the targets, TheThe joint CFAR detection result of certain directionmisses missessome some information of ship the ship targets, so the “OR” operation is used to fuse the detection results in the four directions to improve the PD. so the “OR” operation is used to fuse the detection results in the four directions the PD. The joint a certain misses some information ofto theimprove ship targets, However, the CFAR FAR isdetection still highresult if we of only use thedirection correlation information of the eight-neighborhood, However, the FAR is still high if we only use the correlation information of the eight-neighborhood, so the “OR” operation is used fuseimages, the detection resultsare in the four directions to improve PD. which is shown in Figure 2b. IntoSAR ship targets presented as a cluster of brightthe pixels. which is shown in Figure 2b. In SAR images, ship targets are presented as a cluster of bright pixels. However, the FAR is still high if we only use the correlation information of the eight-neighborhood, However, the strong speckle is presented as isolated bright pixels. Moreover, they are randomly However, strong speckle as ship isolated bright pixels. Moreover, arethe randomly which isthe shown in Figure 2b.isInpresented SAR images, are presented as a information cluster they of bright pixels. distributed. The above characteristics motivate us totargets exploit more correlation of ship However, the strong speckle is presented as isolated bright pixels. Moreover, they are randomly distributed. The above characteristics motivate us to exploit more correlation information of the ship targets in a wider neighborhood. A simulation is done to show this. Figure 2a is the TerraSAR-X distributed. The above characteristics motivate us to exploit more correlation information of the ship targets in aone wider simulation is done toFigure show2b–e this.isFigure 2aCFAR is thedetection TerraSAR-X image, ship neighborhood. target and strongAspeckle are presented. the joint targets in a wider neighborhood. A simulation to show this. Figure 2aCFAR is The thedetection TerraSAR-X image, oneobtained ship target and strong speckle are presented. 2b–e isrespectively. the joint results results with a neighboring distance of is 1, done 2, 3,Figure and 4 pixels, joint CFAR image,with one target and distance strong speckle presented. Figure 2b–e theThe joint CFAR detection detection results are obtained by fusing the2,are detection in the fourisdirections using the “OR” obtained aship neighboring of 1, 3, and 4 results pixels, respectively. joint CFAR detection results obtained a neighboring distance of 1, 2, 3,ship andtarget 4 pixels, The joint CFAR operation. Underwith different distances, canrespectively. be detected, while theoperation. false results are obtained by fusingneighboring the detection resultsthe in the four directions using the “OR” detection results are obtained by fusing the detection results in the four directions using the “OR” alarms are randomly distributed. We can further fuse the detection results using the “AND” Under different neighboring distances, the ship target can be detected, while the false alarms are operation.toUnder neighboring distances, the2f.ship target can be detected, while the false operation lowerdifferent the FAR, is shown indetection Figure randomly distributed. We canwhich further fuse the results using the “AND” operation to lower alarms are randomly distributed. We can further fuse the detection results using the “AND” the FAR, which is shown in Figure operation to lower the FAR, which2f. is shown in Figure 2f.

(a)

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(e)

(f)

Figure 2. Joint(d) CFAR detection results with different image. (e) neighboring distances: (a) the TerraSAR-X (f) One large ship and strong speckle are presented, (b–e) are the joint CFAR detection results with a Figure 2. Joint CFAR detection results with different different neighboring distances: (a)by thefusing TerraSAR-X image. neighboring distance of 1, 2, 3, and 4 with pixels, respectively. They are obtained the results in Figure 2. Joint CFAR detection results neighboring distances: (a) the TerraSAR-X image. Onefour large ship andusing strongthe speckle are presented, (b–e) are the jointdetection CFAR detection results with a the directions “OR” operation. (f) is the joint CFAR result by fusing (b–e) One large ship and strong speckle are presented, (b–e) are the joint CFAR detection results with a −4 specified neighboring distance of 1, 2,A 3,10 and 4 pixels, PFA respectively. They are obtained by fusing the results in using the “AND” operation. is applied. neighboring distance of 1, 2, 3, and 4 pixels, respectively. They are obtained by fusing the results in the the four directions using the “OR” operation. (f) is the joint CFAR detection result by fusing (b–e) four directions using the “OR” operation. (f) is the joint CFAR detection result by fusing (b–e) using −4 using the “AND” operation. −4 A 10 specified PFA is applied.

the “AND” operation. A 10

specified PFA is applied.

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on our ourprevious previouswork work [15], proposed TS-2DLNCFAR detector extends the Based on [15], the the proposed TS-2DLNCFAR detector extends the eighteight-neighborhood to a wider one. Comprehensively considering a high PD and a low FAR, an optimal neighborhood to a wider one. Comprehensively considering a high PD and a low FAR, an optimal window can can be selected, and theand jointthe CFAR withresults different neighboring size of ofthe thetest test window be selected, jointdetection CFAR results detection with different distances aredistances obtainedare using the “OR” operation. the Finally, “AND” the operation used to fuse the neighboring obtained using the “OR”Finally, operation. “AND”isoperation is used detection results with different neighboring distances. Undoubtedly, the proposed joint CFAR detection to fuse the detection results with different neighboring distances. Undoubtedly, the proposed joint methoddetection can acquire a high PD and a low FAR. CFAR method can acquire a high PD and a low FAR. 3. The The Proposed Proposed TS-2DLNCFAR TS-2DLNCFAR Detector 3. Detector Figure 33 illustrates illustratesthethe detection flowchart of proposed the proposed TS-2DLNCFAR detector, Figure detection flowchart of the TS-2DLNCFAR detector, which which includes clutter truncation, parameter estimation, threshold calculation, joint CFAR detection includes clutter truncation, parameter estimation, threshold calculation, joint CFAR detection decision, and and fusion. fusion. TS-2DLNCFAR TS-2DLNCFAR firstly firstly applies applies clutter clutter truncation truncation in in the the background background window. window. decision, Joint CFAR CFAR detection is Joint detection results results with with different different neighboring neighboring distances distances (one (one pixel pixel neighboring neighboring distance distance is abbreviated as (1) in the flowchart, etc.) are acquired using the adaptively-truncated clutter statistics, abbreviated as (1) in the flowchart, etc.) are acquired using the adaptively-truncated clutter statistics, and the the final and final result result is is obtained obtained by by fusing fusing the the detection detection results results with with different different neighboring neighboring distances distances using the the “AND” “AND” operation. Each part part will will be be introduced introduced in using operation. Each in detail detail in in the the later later sections. sections.

Figure detector. Figure 3. 3. Joint Joint CFAR CFAR detection detection flowchart flowchart of the proposed TS-2DLNCFAR detector.

3.1. in the the Background Background Window Window 3.1. Adaptive Adaptive Clutter Clutter Truncation Truncation in The which is is The proposed proposed TS-2DLNCFAR TS-2DLNCFAR uses uses log-normal log-normal as as the the statistical statistical model model of of the the clutter, clutter, which defined as: defined as: ! 1 (ln( x ) − µln )2 2  x>0 pc ( x ) = √ 1 exp  − ln  x   2 (5) 2σln ln  x  0 pc  x   2πσln · x exp   (5) 2





2  x





2 ln

ln  where x is the gray intensity of the clutter, µln and σln is the mean and standard deviation of mean and standard deviation of logwhere x is thelngray intensity of the log-intensity relation to clutter, the mean σ of intensity x is derived as: lnµ and standard  ln is thedeviation ( x ). Their intensity l n  x  . Their relation to the mean  and σ r standard deviation   of intensity x is derived as:

µ = e(µln +σln    e

2 /2)

ln  ln

2

/2

, σ=

,

2

2

e(2µln +σln2 ) · eσln − 1

  e

2 

ln   ln





 e

 ln 2

(6) (6)



1

Undoubtedly, the log-intensity value ln( x ) follows the Gaussian distribution: Undoubtedly, the log-intensity value l n  x  follows the Gaussian distribution: ! 1 (y − µln ) 22 pc (y = ln( x )) = √ 1 exp −  y  2   p y  ln x  2πσln exp   2σln ln 



 

 2 ln 2    So, traditional CFAR detection based on a log-normal distribution can be regarded as: c

2 ln

So, traditional CFAR detection based on a log-normal distribution can be regarded as: ! ! Z∞ Z∞ 2 2ln ) 1 1 y − µ (lnln ( x )x−µln ) 22  (     −y  ln   1 exp −    √ √1 PFA = = exp dy ln  2 dy dx exp   PFA  2πσln · x exp   2σln 2 2 dx  2σ 2πσln 2 ln T



T

2 ln  x

 

2 ln

 

 ln( T ) 2 

ln  T 

ln

 

2 ln

 

(7) (7)

(8) (8)

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where PFA is the probability of false alarm, so z = and Equation (8) can be further expressed as: PFA =

Z∞ t

ln( x )−µln σln

obeys the standard normal distribution,

    Z∞   z2 1 2 t 1 1 1 √ exp − √ exp −w2 dw = − er f √ dz = 2 2 √ 2 2 π 2π 2

(9)

t/ 2

where t is the scale factor, and er f (·) is the error function, which is defined as: 2 er f (t) = √ π

Zt



exp − x

2



0

2 dx = 1 − √ π

Z∞

  exp − x2 dx

(10)

t

Accordingly, for the pixel under test (PUT) with intensity I0 in the test window, it is detected according to the following decision rule: H1

ln( I0 ) − µln > z= t ≤ σln

(11)

H0

H1

ln( I0 )

> µ + t · σln ≤ ln

(12)

H0

where H1 is the hypothesis that the PUT is a target pixel, and H0 is the hypothesis that the PUT is a clutter pixel. The guard window in traditional CFAR detectors is set to avoid the interfering target contamination to the clutter samples in the background window. However, in practice, this is ineffective, especially in multiple target situations. The reference window of the proposed TS-2DLNCFAR only comprises a test window and a background window. Inspired by the CFAR detection methodology, the clutter samples in the background window are truncated using an adaptive threshold to eliminate the high-intensity outliers. The threshold is adaptive to the changing background clutter, as shown in Equation (12). The adaptive threshold based clutter truncation is detailed as follows:

• •

Calculate the mean µ B−ln and standard deviation σB−ln in the log-intensity domain using all samples of the background window. Truncate the clutter samples in the background window using an adaptive threshold. Suppose the gray intensity of a pixel in the background window is IB , if it satisfies Equation (13), it will be excluded from the truncated clutter samples. ln( IB ) ≥ µ B−ln + t1 · σB−ln

(13)

where t1 is the truncation degree, which is vital to the performance of TS-2DLNCFAR. The lower t1 is, the better the high-intensity outliers can be removed from the truncated clutter, but the more the real clutter is eliminated. Since the log-intensity of the clutter obeys the Gaussian distribution, using the adaptive threshold-based clutter truncation, the proportion of the real clutter preserved in all real clutter Rc1 is derived as: !   Z∞ 1 1 1 t1 ( x − µln ) 2 √ √ Tc1 = 1 − exp − dx = + er f (14) 2 2 2σln 2 2πσln 2 µln +t1 ·σln

A plot of Tc1 against t1 is shown in Figure 4a. When t1 ≥ 1.3, Rc1 is as high as 90%; when t1 ≥ 1.9, 97% of the real clutter will be preserved; when t1 ≥ 2.3, Tc1 approaches 99%. A test is implemented to

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95 100

0.1 0.15

90 95

0.05 0.1

85 90

0.05 Tc1 / Tc2（dB） Tc1 / Tc2（dB）

The proportion of the truncated clutter Tc1 The proportion of the truncated clutter Tc1

Sensorsthe 2017, 17, 686 8 of 19 show good real clutter preserving capability of the adaptive threshold-based clutter truncation. The test selects a pure clutter region from the Envisat-ASAR image, and a plot of Tc1/Tc2 against8 tof1 19 is Sensors 2017, 17, 686 proportion of the preserved pixels in all pixels. From Figure 4b, we can reach the conclusion: Tc2 shown in Figure 4b. The real clutter preserving rate Tc2 is defined as the proportion of the preserved coincides Tc1, the deviation nocan more than 0.3conclusion: dB. proportion of the preserved pixels in all pixels. From Figure 4b, can reach the conclusion: Tc2 pixels in allwith pixels. From Figure 4b,iswe reach the Tc2we coincides with Tc1, the deviation coincides with Tc1, the deviation is no more than 0.3 dB. is no more than 0.3 dB. 100 0.15

80 85 75 80 70 75 65 70

0

-0.05 0 -0.1 -0.05 -0.15 -0.1 -0.2 -0.15

60 65

-0.25 -0.2

55 60

-0.3 -0.25

50 55 0 50

0

1 1

2 2

3 4 5 6 7 The truncation depth factor t1 3 4 5 6 7 The truncation depth factor t1

8

9

10

-0.35 -0.3 0 -0.35

8

9

10

0

1 1

2 2

(a)

3 4 5 6 7 The truncation depth factor t1 3 4 5 6 7 The truncation depth factor t1

8 8

9 9

10 10

(b)

(a) (b) Figure 4. Real clutter preserving property analysis: (a) proportion of the preserved real clutter in all Figure 4. Real clutter preserving property analysis: (a) truncation proportiondegrees of the preserved real clutter in all real clutter Tc1; and (b) Tc1/Tc2 value under different (in decibels). Figure 4. Real clutter preserving property analysis: (a) proportion of the preserved real clutter in all real clutter Tc1; and (b) Tc1/Tc2 value under different truncation degrees (in decibels). real clutter Tc1; and (b) Tc1/Tc2 value under different truncation degrees (in decibels).

Comprehensively considering real clutter preservation and high-intensity outlier elimination, the Comprehensively optimal value of considering selected the intersection point of the outlier distributions of the t1 should bereal clutteras preservation and high-intensity elimination, background clutter high-intensity is illustrated Figure canofeasily the optimal of tof should be selected as theoutliers, intersection point of the distributions of5. theWe background the optimalvalue value should be selected as the which intersection point ofinthe distributions the t1 the 1and obtain the distribution of the background clutter, but the statistical distribution of the high-intensity clutter and the high-intensity outliers, which is illustrated in Figure 5. We can easily obtain the background clutter and the high-intensity outliers, which is illustrated in Figure 5. We can easily outliers difficult to of obtain. Unfortunately, thebut optimal threshold is the difficult obtain using the distribution of the background clutter, butclutter, the statistical of high-intensity outliers is obtain theisdistribution the background thedistribution statistical distribution oftothe high-intensity intersection point. Nevertheless, inspired by the CFAR detection methodology, we can choose difficult to obtain. Unfortunately, the optimal threshold is difficult to obtain using the intersection outliers is difficult to obtain. Unfortunately, the optimal threshold is difficult to obtain using thea relatively high realNevertheless, clutter preservation 97%; detection then t1 we can bechoose adaptively calculated point. Nevertheless, inspired by theinspired CFARrate detection methodology, can a relatively highusing reala intersection point. bysuch the as CFAR methodology, we can choose clutter preservation rate such as 97%; then can be using Equation (14). using Equation (14). real clutter relatively high preservation ratet1such as adaptively 97%; then calculated calculated t can be adaptively 1

Equation (14).

Figure Figure5.5.Optimal Optimalthreshold thresholdselection. selection.

Figure 5. Optimal threshold selection.

However,ifift t1is is selected toohigh, high,one oneiteration iterationcannot cannotcompletely completelyeliminate eliminatethe thehigh-intensity high-intensity However, selected too 1 outliers in the the ifbackground background window, we can apply During each iteration, part of the outliers in weone can apply itcannot ititeratively. iteratively. During each iteration, part of However, too high, iteration completely eliminate the high-intensity t1 is selected high-intensity outliers can be eliminated, andapply the and standard deviation in the next iteration the high-intensity outliers can be eliminated, andmean mean andDuring standard in the outliers in the background window, we can itthe iteratively. eachdeviation iteration, part ofnext the become smaller, so the high-intensity outliers preserved in the former iteration can be further iteration become smaller, so the high-intensity outliers preserved in the former iteration can be high-intensity outliers can be eliminated, and the mean and standard deviation in the next iteration eliminated. After several iterations, the high-intensity outliers can be eliminated completely, and the further several iterations, the high-intensity can be eliminated becomeeliminated. smaller, soAfter the high-intensity outliers preserved inoutliers the former iteration can completely, be further real clutter After can be preserved to thethe largest degree. Figure 6 illustrates the relation between and the the real eliminated. several iterations, high-intensity outliers can be eliminated completely, clutter preservation rate and the iteration number, where is set to 1.9 to preserve 97% of the real t real clutter can be preserved to the largest degree. Figure 6 1illustrates the relation between the real clutter preservation rate and the iteration number, where t1 is set to 1.9 to preserve 97% of the real

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and the real clutter can be preserved to the largest degree. Figure 6 illustrates the relation between 9 of 19 the real clutter preservation rate and the iteration number, where t1 is set to 1.9 to preserve 97% of the real clutter. iterations, outliers completely eliminated, andnearly nearly97% 97%ofofthe the real real clutter. AfterAfter five five iterations, the the outliers cancan be be completely eliminated, and clutter is preserved, which is shown in Figure 13b,c. clutter is preserved, which is shown in Figure 13b,c. Sensors 2017, 17, 686

Figure Figure6. 6.Relation Relationbetween betweenthe thereal realclutter clutterpreservation preservation rate rate and and the the iteration iteration number. number.

3.2. 3.2. Parameter Parameter Estimation Estimation of of the the Truncated Truncated Clutter Clutter





XX  = X1{, X obey Suppose the local reference window areare Supposethe theclutter cluttersamples samplesinin the local reference window X21,, X2X, ·Nc· · ,Xthey they all Nc }, all obeysame the same probability density function (PDF) f X ( xand cumulativedistribution distributionfunction function(CDF) (CDF) ) andcumulative the probability density function (PDF) fX x FX ( x ). After adaptive threshold-based clutter truncation, the truncated clutter samples become FeX  x  . After adaptive threshold-based clutter truncation, the truncated clutter samples become X = { xe1 , xe2 , · · · xen }. They obey the same PDF f Xe ( x, t1 ), and the PDF in the log-intensity domain of the truncated f Xe (y = ln(the x ), tsame be expressed X  x1, x2,clutter xn . They 1 ) canPDF obey , and the PDF in the log-intensity domain of the f  x , t as:





X



1



 f X ( xas: ) truncated clutter f X y  ln x , t1 can be  expressed , y ≤ µln + t1 · σln F µ + t ( X ln 1 · σln ) f Xe (y = ln( x ), t1 ) =   fX  x 0, , yy >µlnln+t1 t1·lnσln  f X  y   ln ( x ), t1    FX2 ln  t1   ln   (ln( x ) − µln )    exp−   2σln 2  0, y  ln  t1   ln   !! , y ≤ µln + t1 · σln t1  2  √2πσ x· 1 +1lner(f x )√ =  ln     lnexp 2 2   22     2 ln    y >,µy +t     0, ln ln1 · σt1ln  ln

(15)

(15)

 1 1  t1    2 ln x    erf   Then the mean and standard deviation in domain are estimated using the 2 2  the2 log-intensity   truncated clutter through the maximum likelihood estimator (MLE) [46]: 0, y  ln  t1   ln

 n  (ln( xei )−µlnare )2 estimated using the Then the mean and standard deviation in the log-intensity∑domain  exp − i=1 [46]: truncated clutter likelihood estimator (MLE) 2σln 2  the maximum  through n e ζ µln , σln X = ∏ f Xe ( xei |µln , σln ) = h (16)   n in nn √ 1 1 2  t1 i =1   x     √ 2πσln  · ∏ xeln · + er f  i ln  i 2 2  i=i 1  2

exp  2 ln 2   A logarithmic operation isn applied to Equation (16), and  the MLE is derived as:    ln , ln X   f X  xi ln , ln   n n n i 1 1 1  t   1  2  ln    xi    erf     i 1  2  2 2





A logarithmic operation is applied to Equation (16), and the MLE is derived as:

(16)

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i h  e ∂ln ζ µln , σln X ∂µln

= 0,

i h  e ∂ln ζ µln , σln X ∂σln

=0

(17)

The mean and standard deviation are estimated by:

µˆ ln

v u 2 u1 n 1 n = ∑ ln( xei ), σˆ ln = t ∑ (ln( xei ) − µˆ ln ) n i =1 n i =1

(18)

Similarly, the spatial correlation coefficients in the four directions using the adaptively-truncated clutter of the local reference window are defined as: M N

∑ ∑ [ f (i, j) − µ][ f (i + l, j + k) − µ] r (l, k ) =

i =1 j =1 M N

∑ ∑ [ f (i, j) − µ]

2

(19)

i =1 j =1

where (i, j), (i + l, j + k ) is included for spatial correlation coefficient estimation only under the condition that both of them belong to the truncated clutter. µ is the gray intensity mean value of the truncated clutter of the local reference window. 3.3. Joint CFAR Detection and Fusion The proposed TS-2DLNCFAR detector uses a 2DLN model as the JPDF of the truncated clutter. The detailed steps are specified as follows:

• • • • • • • •

Input the PFA, the sizes of the background window, and the test window. Obtain the truncated clutter using the adaptive threshold based clutter truncation introduced in Section 3.1. Estimate the mean µˆ ln , standard deviation σˆ ln , and the spatial correlation coefficients in the four directions using the truncated clutter through Equations (18) and (19). Establish the JPDF in the four directions through Equation (1), and calculate the joint CFAR detection thresholds in the four directions through Equation (3). Joint CFAR detection is applied to the pixels under test in the test window using Equation (4). Let the local reference window slide on the SAR image, and obtain the four joint CFAR detection results in the four directions with a certain neighboring distance. The joint CFAR detection result of a certain neighboring distance is obtained by fusing the detection results in the four directions using the “OR” operation. All detection results of different neighboring distances are acquired, and the final detection result is obtained by fusing the detection results of different neighboring distances using the “AND” operation.

4. Experimental Results and Analysis In order to validate the excellent detection performance of the proposed TS-2DLNCFAR in high-intensity outliers’ presented areas, such as crowded harbors, the low-resolution, multi-look, VV polarized, C-band, amplitude Envisat-ASAR image (shown in Figure 7) and the high-resolution, multi-look, HH polarized, X-band, amplitude TerraSAR image (shown in Figure 8) are employed in this study. The Envisat-ASAR image was acquired by the IM mode on 20 July 2007 over the Qingdao harbor, of which the resolution is 30 m and the number of looks is 10. The TerraSAR-X image was acquired by the StripMap (SM) mode on 31 July 2009 over the Panama Canal, of which the resolution is 3 m and the number of looks is 50. We select the area of densely-distributed ship targets near the Qingdao harbor (the rectangle-marked area in Figure 7) and the ghosts and side-lobes presented area near the Panama

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canal (the rectangle marked area in Figure 8) to validate the detection performance. Since TS-CFAR outperforms other CFAR detectors in multiple target situations [42], TS-CFAR is selected to validate the better Sensors detection performance of the proposed TS-2DLNCFAR. Moreover, CA-CFAR [13], NM-CFAR 2017, 17, 686 11 of 19 [14], Sensors 2017,K-CFAR 17, 686 11 of 19 of the LN-CFAR [14], [10], and 2DLN-CFAR [15] are used for comparison to show the superiority selected to validate the better detection performance of the TS-2DLNCFAR. Moreover, proposed TS-2DLNCFAR. The experimental parameters are setproposed as follows:

•

•

•

selected to [13], validate the better detection performance of the proposed TS-2DLNCFAR. Moreover, CA-CFAR NM-CFAR [14], LN-CFAR [14], K-CFAR [10], and 2DLN-CFAR [15] are used for CA-CFAR [13], NM-CFAR [14], LN-CFAR [14], K-CFAR [10], and 2DLN-CFAR [15] are for use comparison to show the superiority of the image: proposed TS-2DLNCFAR. The experimental parameters are For the low-resolution Envisat-ASAR CA-CFAR, NM-CFAR, LN-CFAR, andused K-CFAR comparison to show the superiority of the proposed TS-2DLNCFAR. The experimental parameters are a set 41 as × follows: 41 reference window with a 21 × 21 guard window and a 1 × 1 test window. 2DLN-CFAR set as follows: uses a 41 41 referenceEnvisat-ASAR window with a 21 × 21 guard window and aand 3 ×K-CFAR 3 test use window.  For the×low-resolution image: CA-CFAR, NM-CFAR, LN-CFAR, TS-CFAR the proposed TS-2DLNCFAR use a window 41 × 41 reference window with no guard  aFor Envisat-ASAR CA-CFAR, NM-CFAR, and2DLN-CFAR K-CFAR useregion, 41the ×and 41low-resolution reference window with a 21 image: × 21 guard and a 1 × 1LN-CFAR, test window. a 41 ×a 41 reference with a 21 a× 21and window and and a 1with ×a 13 test window. 2DLN-CFAR uses ×with 41 reference with ×guard 21 TS-2DLNCFAR guard window ×a3 3test but TS-CFAR a 1window × window 1 test window ×window. 3, 5 × 5,TS-CFAR 7 × 7, 9 × 9, uses a 41 × 41 reference window with a 21 × 21 guard window and a 3 × 3 test window. TS-CFAR and the proposed TS-2DLNCFAR use a 41 × 41 reference window with no guard region, but TSand 11 × 11 test window. and thewith proposed a 41 × 41 reference region, TSCFAR a 1 × 1 TS-2DLNCFAR test window anduse TS-2DLNCFAR with awindow 3 × 3, 5 ×with 5, 7 no × 7,guard 9 × 9, and 11 ×but 11 test For the high-resolution TerraSAR-X image: CA-CFAR, NM-CFAR, LN-CFAR, and K-CFAR use an CFAR with a 1 × 1 test window and TS-2DLNCFAR with a 3 × 3, 5 × 5, 7 × 7, 9 × 9, and 11 × 11 test window. 81 × For 81 reference window with a 41 × 41 guard window and a 1 × 1 test window. 2DLN-CFAR window. the high-resolution TerraSAR-X image: CA-CFAR, NM-CFAR, LN-CFAR, and K-CFAR use uses an 81 × 81 reference window with 41 ×window 41 guard aand 3× 3 test use window.  an For81 the high-resolution TerraSAR-X image: CA-CFAR, NM-CFAR, K-CFAR × 81 reference window with a 41 × 41aguard and window a 1 × LN-CFAR, 1 testand window. 2DLN-CFAR TS-CFAR proposed TS-2DLNCFAR an window 81 × 81and window with no guard an 81an ×and 81 window withwith a 41 a× 41 41 ×guard window and a reference 1 ×a13 test window. 2DLN-CFAR uses 81 reference ×the 81 reference window 41use guard × 3 test window. TS-CFAR usesbut an 81 × 81 reference awindow 41 and with a 3 × 3no test window. and the proposed TS-2DLNCFAR use 81××41 81guard reference window guard region, TS-CFAR uses window a 1 × 1with testan andwindow TS-2DLNCFAR uses a 3region, × 3,TS-CFAR 5but ×TS5, 7 × 7, and theuses an 81 × 81 reference region, TS1 ×test 1 TS-2DLNCFAR test window anduse TS-2DLNCFAR uses a window 3 × 3, 5 ×with 5, 7 ×no 7, guard 9 × 9, and 21 ×but 21 test 9 × 9,CFAR and 21proposed ×a21 window. CFAR uses a 1 × 1 test window and TS-2DLNCFAR uses a 3 × 3, 5 × 5, 7 × 7, 9 × 9, and 21 × 21 test window. For TS-CFAR, the truncation depth is set to 25%, the same as that given by Ding et al. [42]. For the window.  For TS-CFAR, the truncation depth is set to 25%, the same as that given by Ding et al. [42]. For the proposed TS-2DLNCFAR, the truncation degree t1 is set to 1.9, and the iteration number is set to 5.  proposed For TS-CFAR, the truncation is set to 25%, the same as1.9, thatand given Ding etnumber al. [42].is For TS-2DLNCFAR, thedepth truncation degree set to theby iteration setthe to t1 is Thus,proposed the high-intensity outliers truncation are eliminated, whereas 97% real clutter samples are preserved TS-2DLNCFAR, to 1.9,of and the number is set to t1 is set 5. Thus, the high-intensitytheoutliers are degree eliminated, whereas 97% of iteration real clutter samples are

for parameter estimation and statistical 5. Thus, the outliersand aremodeling. eliminated, whereas 97% of real clutter samples are preserved for high-intensity parameter estimation statistical modeling. preserved for parameter estimation and statistical modeling.

Figure 7. Low-resolution, multi-look, VV polarized SAR image of Qingdao harbor region acquired by

Figure 7. Low-resolution, multi-look, VV polarized SAR image of Qingdao harbor region acquired by Figure 7. Low-resolution, VV the C-band Envisat-ASARmulti-look, IM mode on 20polarized July 2007.SAR image of Qingdao harbor region acquired by the C-band Envisat-ASAR IM mode on 20 July 2007. the C-band Envisat-ASAR IM mode on 20 July 2007.

Figure 8. High-resolution, multi-look, HH polarized SAR image of the Panama Canal region acquired Figure 8. High-resolution, multi-look, polarized X-band TerraSAR SM mode on HH 31 July 2009. SAR image of the Panama Canal region acquired Figureby 8.the High-resolution, multi-look, HH polarized SAR image of the Panama Canal region acquired by the X-band TerraSAR SM mode on 31 July 2009.

by the X-band TerraSAR SM mode on 31 July 2009.

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A comparative analysis of the CFAR detectors is shown in Figures 9 and 10 with a 10−4 specified PFA. The detection results of CA-CFAR are not shown because no pixel is detected. 9a is the A comparative analysis of the CFAR detectors is shown in Figures 9 and 10 with a Figure 10-4 specified original Envisat-ASAR image (350 × 400), there are 12 densely-distributed targets PFA. The detection results of CA-CFAR areand not shown because no pixel is detected.ship Figure 9a is in thethe image. Traditional CFARimage detectors as CA-CFAR, K-CFAR, LN-CFAR, and ship 2DLN-CFAR original Envisat-ASAR (350such × 400), and there are 12 densely-distributed targets inuse the all pixels in the background window for parameter estimation, so the parameters are overestimated image. Traditional CFAR detectors such as CA-CFAR, K-CFAR, LN-CFAR, and 2DLN-CFAR use all as a result interfering targets’ As a consequence, PD degrades dramatically, pixels of in the background windowcontamination. for parameter estimation, so the parameters are overestimated as as a resultCA-CFAR of the interfering targets’ contamination. a consequence, PD degrades as shown. misses all 12 targets, K-CFAR As misses three, LN-CFAR missesdramatically, six, 2DLN-CFAR shown. CA-CFAR misses all 12 targets, K-CFAR misses three, LN-CFAR misses six, 2DLN-CFAR misses one, and some detected ship targets are incomplete. NM-CFAR uses a Gaussian statistical misses one,clutter, and some detected targets incomplete. NM-CFAR uses a As Gaussian model of the which cannotship describe theare long-tail property of the clutter. a result,statistical the FAR is model of thehigh, clutter, which cannot describe long-tail property of the clutter. As a and result, FAR unreasonably which reaches 0.252%, 14 the dB larger than the given PFA. TS-CFAR thethe proposed is unreasonably high, which reaches 0.252%, 14 dB larger than the given PFA. TS-CFAR and the of TS-2DLNCFAR can detect all of the ship targets using clutter truncation, but TS-CFAR has a FAR proposed TS-2DLNCFAR can detect all of the ship targets using clutter truncation, but TS-CFAR has − 4 − 5 3 × 10 (42 false alarms) compared with 4 × 10 (five false alarms) of the proposed TS-2DLNCFAR a FAR of 3 × 10−4 (42 false alarms) compared with 4 × 10−5 (five false alarms) of the proposed TSwith a 3 × 3 test window. With the increasing size of the test window, the FAR of the proposed 2DLNCFAR with a 3 × 3 test window. With the increasing size of the test window, the FAR of the TS-2DLNCFAR decreases. This is because the strong speckle is presented as isolated bright pixels, proposed TS-2DLNCFAR decreases. This is because the strong speckle is presented as isolated bright and ship targets are presented as a cluster of bright pixels with a certain length and width. Thus, pixels, and ship targets are presented as a cluster of bright pixels with a certain length and width. when the neighboring distance becomes larger, TS-2DLNCFAR can exclude the false alarms effectively. Thus, when the neighboring distance becomes larger, TS-2DLNCFAR can exclude the false alarms However, if the selected size of the test window is too large, the PD degrades. In Figure 9h–j, all targets effectively. However, if the selected size of the test window is too large, the PD degrades. In Figure can9h–j, be detected using 3× 3, 5 × 5,using and 37 ××3,7 5test whenhowever, the size when of the the testsize window all targets can be detected × 5,windows, and 7 × 7 however, test windows, of is larger 7 × 7, some parts the shipparts targets areship missed, asare shown in Figure 9k,l. the testthan window is larger than 7of × 7, some of the targets missed, as shown in Figure 9k–l.

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(e)

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(g)

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Figure 9. 9. Detection on aa region region of of densely-distributed densely-distributed ship targets: Figure Detectionperformance performancecomparison comparison on ship targets: (a)(a) thethe multi-look Envisat-ASAR are densely denselydistributed; distributed;(b) (b)ground ground truth; NM-CFAR; multi-look Envisat-ASARimage, image, 12 12 targets targets are truth; (c)(c) NM-CFAR; (d)(d) K-CFAR; (e)(e)LN-CFAR; and(h–l) (h–l)are arethe thedetection detection results K-CFAR; LN-CFAR;(f) (f)TS-CFAR; TS-CFAR; (g) (g) 2D-LNCFAR; 2D-LNCFAR; and results of of thethe proposed TS-2DLNCFAR 7, 99 ××9,9,and and11 11××1111test testwindows, windows, truncation proposed TS-2DLNCFARwith witha a3 3××3,3,55×× 5, 5, 77 × × 7, thethe truncation −-44 specified PFA is applied. degree is is setset toto 1.9. degree 1.9.AA1010 specified PFA is applied.

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Figure 280). There There is is one one large large ship, ship, two two small small ships, ships, Figure 10a 10a is is the the original original TerraSAR-X TerraSAR-Ximage image(280 (280×× 280). and two “ghosts” caused by the low PRF. CA-CFAR again misses all the ship targets. NM-CFAR, and two “ghosts” caused by the low PRF. CA-CFAR again misses all the ship targets. NM-CFAR, KK-CFAR, LN-CFAR,TS-CFAR, TS-CFAR,2DLN-CFAR, 2DLN-CFAR,and andthe theproposed proposedTS-2DLNCFAR TS-2DLNCFAR can can detect detect all all of CFAR, LN-CFAR, of the the ship targets. However, NM-CFAR suffers a high FAR, many clutter pixels are regarded as targets. ship targets. However, NM-CFAR suffers a high FAR, many clutter pixels are regarded as targets. LN-CFAR and K-CFAR K-CFARsuffer suffera arelatively relatively higher FAR, there a large number false alarms LN-CFAR and higher FAR, there are aare large number of falseofalarms caused caused by side-lobes and ghosts. TS-CFAR suffers a higher FAR than LN-CFARand andK-CFAR K-CFAR for for the by side-lobes and ghosts. TS-CFAR suffers a higher FAR than LN-CFAR the exclusion exclusion of of the the high-intensity high-intensity real real clutter clutter samples. samples. 2DLN-CFAR 2DLN-CFAR and and the the proposed proposed TS-2DLNCFAR TS-2DLNCFAR comprehensively comprehensivelyuse usethe the contrast contrast and and the the correlation correlation information, information,so so they they can can detect detect all all of of the the targets targets with a lower FAR. However, 2DLN-CFAR misses some parts of the large ship target. When with a lower FAR. However, 2DLN-CFAR misses some parts of the large ship target. When the the size size of of the the test test window window is is larger, larger, the the FAR FAR of of TS-2DLNCFAR TS-2DLNCFAR becomes becomes lower, lower, while while the the PD PD is is still still high. high. However, However, when when the the size size is is as aslarge largeas as21 21×× 21, 21, all all of of the the small small targets targets are are missed, missed, whereas whereas the the large large ship target can be detected. The proposed TS-2DLNCFAR achieves the best detection performance ship target can be detected. The proposed TS-2DLNCFAR achieves the best detection performance if ifthe thesize sizeofofthe thetest testwindow windowisisselected selectedproperly. properly. In In aa real real application, application, we we can can obtain obtain the the minimum minimum size size of of the the ships ships to to be be detected detected in in the the SAR SAR image, image, and and the the best best size size of of the the test test window window can can be be selected selected as as the the minimum minimum size size of of the the ships ships to to be be detected. detected. However, However, if if the the minimum minimum size size of of the the ship ship target target is is not known, comprehensively considering the PD and FAR, we can select a small size such as 5 × 5 or not known, comprehensively considering the PD and FAR, we can select a small size such as 5 × 5 or 77 × to get get aa relatively relatively promising promising detection detection result. result. × 77 to

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Figure Detectionperformance performancecomparison comparisonononghosts ghosts and side-lobes presented region: Figure 10. 10. Detection and side-lobes in in thethe presented region: (a) (a) the multi-look TerraSAR-X image. One large ship, two small ship targets, and two “ghosts” the multi-look TerraSAR-X image. One large ship, two small ship targets, and two “ghosts” are are presented; K-CFAR; (e) LN-CFAR; (f) TS-CFAR; (g) 2D-LNCFAR; presented; (b) (b) ground ground truth; truth; (c) (c) NM-CFAR; NM-CFAR; (d) (d) K-CFAR; (e) LN-CFAR; (f) TS-CFAR; (g) 2D-LNCFAR; and (h–l) are the detection results of the proposed TS-2DLNCFAR with a 3 × 3, 5 × 5, 9× 9, and (h–l) are the detection results of the proposed TS-2DLNCFAR with a 3 × 3, 5 × 5, 7 ×77,×97,× 9, and and 21 × 21 test windows, the truncation degree is set to 1.9. −4 A 10−4 specified PFA is applied. 21 × 21 test windows, the truncation degree is set to 1.9. A 10 specified PFA is applied.

Since the PFA is not low enough, Figure 10 cannot demonstrate TS-2DLNCFAR’s superiority on high PD in ghosts and side-lobes’ presented backgrounds. Here, we lower the PFA to 10−9, and the

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Since the PFA is not low enough, Figure 10 cannot demonstrate TS-2DLNCFAR’s superiority on 14 of 19 high PD in ghosts and side-lobes’ presented backgrounds. Here, we lower the PFA to 10−9 , and the detection results results of of the thesix sixCFAR CFAR detectors detectors are areshown shownin inFigure Figure11. 11.NM-CFAR NM-CFARstill stillsuffers suffersaahigh highFAR, FAR, detection and CA-CFAR misses all of the ships. K-CFAR misses one small ship target, LN-CFAR and K-CFAR and CA-CFAR misses all of the ships. K-CFAR misses one small ship target, LN-CFAR and K-CFAR miss some some parts misses thethe large ship target. TS-CFAR andand the miss parts of of the thelarge largeship shiptarget, target,and and2DLN-CFAR 2DLN-CFAR misses large ship target. TS-CFAR proposed TS-2DLNCFAR with awith 5 × 5a test can detect of the all shipoftargets, buttargets, TS-2DLNCFAR the proposed TS-2DLNCFAR 5 × window 5 test window canalldetect the ship but TShas a lower FAR compared with TS-CFAR. 2DLNCFAR has a lower FAR compared with TS-CFAR. Sensors 2017, 17, 686

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Figure comparison onon ghosts andand side-lobes in the presented region: (a) Figure 11. 11. Detection Detectionperformance performance comparison ghosts side-lobes in the presented region: the multi-look TerraSAR-X image. One large ship, two small (a) the multi-look TerraSAR-X image. One large ship, two smallship shiptargets, targets,and andtwo two “ghosts” “ghosts” are are presented; (b) ground truth; (c) NM-CFAR; (d) K-CFAR; (e) LN-CFAR; (f) TS-CFAR; (g) 2D-LNCFAR; presented; (b) ground truth; (c) NM-CFAR; (d) K-CFAR; (e) LN-CFAR; (f) TS-CFAR; (g) 2D-LNCFAR; and and (h) (h) the the proposed proposed TS-2DLNCFAR TS-2DLNCFAR with with aa 55 ××55test testwindow, window,and andthe thetruncation truncationdegree degreeisisset setto to1.9. 1.9. −9 A A 10 10−9specified specifiedPFA PFAisisapplied. applied.

The detection performance is further verified by the goodness-of-fit test for each statistical The detection performance is further verified by the goodness-of-fit test for each statistical model, model, as illustrated in Figure 12. Since the proposed TS-2DLNCFAR and 2DLN-CFAR use 2DLN as illustrated in Figure 12. Since the proposed TS-2DLNCFAR and 2DLN-CFAR use 2DLN distribution distribution to model the JPDF of the sea clutter, it is not suitable to compare with the statistical to model the JPDF of the sea clutter, it is not suitable to compare with the statistical models used by models used by conventional CFAR detectors. However, we can use the log-normal model to show conventional CFAR detectors. However, we can use the log-normal model to show the better statistical the better statistical modeling property through adaptive threshold-based clutter truncation. For CAmodeling property through adaptive threshold-based clutter truncation. For CA-CFAR, LN-CFAR, CFAR, LN-CFAR, K-CFAR, and 2DLN-CFAR, caused by the contamination of the interfering ship K-CFAR, and 2DLN-CFAR, caused by the contamination of the interfering ship targets, the statistical targets, the statistical models deviate from the histogram significantly. Both TS-CFAR and the models deviate from the histogram significantly. Both TS-CFAR and the proposed TS-2DLNCFAR proposed TS-2DLNCFAR apply clutter truncation firstly, so the statistical models are more accurate. apply clutter truncation firstly, so the statistical models are more accurate. However, the proposed However, the proposed TS-2DLNCFAR has a better fitting performance with a KL distance of 0.0289, TS-2DLNCFAR has a better fitting performance with a KL distance of 0.0289, compared with 0.1392 compared with 0.1392 acquired by TS-CFAR. The above phenomenon can be described by the fact acquired by TS-CFAR. The above phenomenon can be described by the fact that 97% of the real clutter that 97% of the real clutter is preserved in the truncated clutter for the proposed TS-2DLNCFAR with is preserved in the truncated clutter for the proposed TS-2DLNCFAR with a truncation degree of a truncation degree of 1.9, while TS-CFAR discards a large amount of high-intensity real clutter with 1.9, while TS-CFAR discards a large amount of high-intensity real clutter with a truncation depth of a truncation depth of 25%, which is shown in Figure 13. Although the estimation error of TS-CFAR 25%, which is shown in Figure 13. Although the estimation error of TS-CFAR is compensated by a is compensated by a normalization factor, the estimated parameters are still biased due to the normalization factor, the estimated parameters are still biased due to the incomplete clutter samples. incomplete clutter samples.

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50 100 Figure 12. Goodness-of-fit test of0 different models. the150black 200 circles 250 represent the histogram, the blue solid, the black dash-dotted, the green dashed, Gray theIntensity pink dash-dotted, and the red dotted are Gaussian solid, the black dash-dotted, the green dashed, the pink dash-dotted, and the redlog-normal dotted are by NM-CFAR, K model by K-CFAR, truncated statistic-based Gamma by TS-CFAR, by Gaussian FigureLN-CFAR 12. Goodness-of-fit test of and different models. the black circles represent histogram, the blue by by NM-CFAR, K model by K-CFAR, truncated statistic-based Gamma bythe TS-CFAR, log-normal and 2DLN-CFAR, adaptively-truncated statistics-based log-normal by the proposed solid, the black dash-dotted, the green dashed, the pink dash-dotted, and the red dotted are Gaussian TS-2DLNCFAR, respectively. LN-CFAR and 2DLN-CFAR, and adaptively-truncated statistics-based log-normal by the proposed by NM-CFAR, K model by K-CFAR, truncated statistic-based Gamma by TS-CFAR, log-normal by TS-2DLNCFAR, respectively. 0.03

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LN-CFAR and 2DLN-CFAR, and adaptively-truncated statistics-based log-normal by the proposed 0 0 50 100 150 200 250 Gray Intensity TS-2DLNCFAR, respectively. Figure 12. Goodness-of-fit test of different models. the black circles represent the histogram, the blue solid, the black dash-dotted, the green dashed, the pink dash-dotted, and the red dotted are Gaussian by NM-CFAR, K model by K-CFAR, truncated statistic-based Gamma by TS-CFAR, log-normal by LN-CFAR and 2DLN-CFAR, statistics-based (a) (b) and adaptively-truncated (c) (d) log-normal by the(e)proposed TS-2DLNCFAR, respectively. Figure 13. Clutter truncation result comparison: (a) the reference window image; (b) the removed pixels using an adaptive threshold of TS-2DLNCFAR with t1 = 1.9, and five iterations; (c) the truncated clutter by TS-2DLNCFAR; (d) the removed pixels by TS-CFAR with a truncation depth of 25%; and (a) (c) (d) (e) (e) the truncated clutter (b) by TS-CFAR.

Figure 13. Clutter truncation result comparison: (a) the reference window image; (b) the removed

Figure 13. Furthermore, Clutter truncation result comparison: (a)using the reference window image; (b) the removed the 2DLN distribution modeled all samples by 2DLN-CFAR is compared pixels using an adaptive threshold of TS-2DLNCFAR with t1 = 1.9, and five iterations; (c) the truncated with that modeled by the proposed TS-2DLNCFARwith using adaptively-truncated clutter. pixels using an adaptive threshold of TS-2DLNCFAR t1 the = 1.9, and five iterations; (c) theFigure truncated clutter by TS-2DLNCFAR; (d) the removed pixels by TS-CFAR with a truncation depth of 25%; and 14a shows the the joint distribution using of the clutter pixels in the background (a) contour of (b) (c)all (d) (e) of 25%; clutter by TS-2DLNCFAR; (d) the removed pixels by TS-CFAR with a truncation depth (e)window, the truncated bytargets TS-CFAR. whereclutter the ship are excluded from the clutter samples. Figure 14b shows the contour and (e) the truncated TS-CFAR. Figure 13.clutter Clutterby truncation result comparison: (a) the reference window image; (b) the removed of the 2DLN model based on the truncated clutter statistics by the proposed TS-2DLNCFAR, where the

= 1.9, and five (c) the truncated pixels using2DLN an adaptive threshold ofmodeled TS-2DLNCFAR with t1samples Furthermore, using allall by iterations; 2DLN-CFAR is compared KL distance is the 0.116. Figuredistribution 14c shows the 2DLN model using of the pixels, including the interfering clutter by TS-2DLNCFAR; (d)TS-2DLNCFAR the removed pixelsusing by TS-CFAR with a truncation depth ofclutter. 25%; andFigure with that modeled by the proposed the adaptively-truncated ship targets by 2DLN-CFAR, which deviates the actual JPDF of the clutter significantly, with a KL Furthermore,(e)the 2DLN distribution modeled using all samples by 2DLN-CFAR isdistance compared with the truncated clutter by TS-CFAR. 14a shows the contour of the joint all2DLN of the clutter the background as large as 1.128. We can easily reachdistribution the conclusionusing model basedpixels on the in truncated clutter that modeled by the proposed TS-2DLNCFAR using that thethe adaptively-truncated clutter. Figure 14a shows statistics hasthe a better fitting performance compared with that without clutterFigure truncation. window, where ship targets are excluded from the clutter samples. 14b shows the contour Furthermore, the 2DLN distribution modeled using all samples by 2DLN-CFAR is compared the contour of the joint distribution using all of the clutter pixels in the background window, where the of the 2DLN model based onbythe statistics using by thethe proposed TS-2DLNCFAR, where the with that modeled thetruncated proposed clutter TS-2DLNCFAR adaptively-truncated clutter. Figure ship KL targets are is excluded from14c the clutter samples. Figure 14b shows the contour of theinterfering 2DLN model distance 0.116. the Figure modelusing usingall allofofthe theclutter pixels,pixels including 14a shows contour shows of the the joint2DLN distribution in thethe background basedship ontargets the window, truncated clutter statistics byexcluded theactual proposed TS-2DLNCFAR, the KL distance is where the ship targets are from theof clutter samples. Figurewhere 14b shows contour by 2DLN-CFAR, which deviates the JPDF the clutter significantly, with athe KL distance of1.128. theshows 2DLN model based on the by the proposed TS-2DLNCFAR, where thetargets 0.116.asFigure theeasily 2DLN model using clutter all that of statistics the including the interfering ship large as14c We can reach thetruncated conclusion thepixels, 2DLN model based on the truncated clutter KLadistance is deviates 0.116.performance Figure 14cactual shows the 2DLN using all significantly, of the pixels, including interfering by 2DLN-CFAR, whichfitting the JPDF ofmodel the withthe a KL distance as statistics has better compared with thatclutter without clutter truncation.

ship targets by 2DLN-CFAR, which deviates the actual JPDF of the clutter significantly, with a KL distance

large as 1.128. We can easily reach the conclusion that the 2DLN model based on the truncated clutter as large as 1.128. We can easily reach the conclusion that the 2DLN model based on the truncated clutter statistics has astatistics betterhas fitting performance compared with without clutter truncation. a better fitting performance compared withthat that without clutter truncation.

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(c) Figure 14. Goodness-of-fit test using the 2DLN model on real SAR data: (a) the joint distribution of

Figure 14.the Goodness-of-fit test using the 2DLN model on real SAR data: (a) the joint distribution of the neighboring pixels in the horizontal direction; (b) 2DLN modeled from the truncated clutter by neighboring pixels inTS-2DLNCFAR; the horizontal (b) 2DLN modeled from the the proposed anddirection; (c) 2DLN modeled without clutter truncation by truncated 2DLN-CFAR.clutter by the proposed TS-2DLNCFAR; and (c) 2DLN modeled without clutter truncation by 2DLN-CFAR. Furthermore, the receiver operating characteristic (ROC) curves are also derived to validate the detection performance of the proposed TS-2DLNCFAR with a 3 × 3 test window. The ROC curves are Furthermore, the Monte receiver operating characteristic (ROC) curves are on also to validate the acquired using Carlo simulations, where each simulation is conducted thederived local reference window with a sample of 1681 (41 × 41 window sizewith including the3PUT). The test image detection performance of the size proposed TS-2DLNCFAR a3× test window. Thewhere ROCa curves are large number of ship targets are densely distributed is selected from Figure 7 with a size of 1020 × 1020. acquired using Monte Carlo simulations, where each simulation is conducted on the local reference Firstly, the local reference windows are obtained with one pixel sliding step on the test image, and window with size of 1681 (41 × 41 size including the PUT). Thewill testbeimage then a thesample boundary pixels are discarded, sowindow 1 × 106 (1000 × 1000) local reference windows sent where a large number of ship targets are densely distributed selected from 7 with window, a size ofand 1020 × 1020. for Monte Carlo simulations. All six CFAR detectorsisare applied on eachFigure local reference we can obtain the final detection binary map with different PFAs. The correctly-detected pixels and Firstly, the local reference windows are obtained with one pixel sliding step on the test image, and then the falsely-detected pixels are counted from6 the detection binary image compared with the ground the boundary pixels are discarded, so 1 × 10 (1000 × 1000) local reference windows will be sent for truth. Finally, the observed false alarm rate P f , and the detection rate Pd can be obtained through [47]:

Monte Carlo simulations. All six CFAR detectors are applied on each local reference window, and we nfa can obtain the final detection binary map with different PFAs. The correctly-detected pixels and the Pf  (20) m n binary nt falsely-detected pixels are counted from the detection image compared with the ground truth. Finally, the observed false alarm rate Pf , and the detection rate Pd can be obtained through [47]: n Pd  d (21) nt nfa where n fa are the observed false alarms, and n are the length and width of the test image m Pf = (20) m × n − nt excluding the boundary pixels, both of which are 1000. n t is the true target pixel number, m  n  nt

is the real clutter pixel number of the test image. n dndis the correctly detected pixel number. Figure

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d 15 shows the derived ROC curves, where the target detection rate Pd is plotted against the observed nt

false alarm rate P . CA-CFAR, LN-CFAR, K-CFAR, and 2DLN-CFAR use all of the samples for

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f where n f a are the observed false alarms, m and n are the length and width of the test image excluding statistical modeling, so the statistical models are quite inaccurate as a result of the high-intensity the boundary pixels, both of which are 1000. nt isPDthe true target pixel number, m × n − n is the real outliers’ contamination. As a consequence, the degrades. Both TS-CFAR and the proposed TS-t clutter pixel number of the test image. n is the correctly detected pixel number. Figure 15 shows the 2DLNCFAR apply clutter truncation firstly, so the statistical models established using the truncated d clutter are more accurate than those without clutter truncation. TS-CFAR discards 25% of the highderived ROC curves, where the target detection rate Pd is plotted against the observed false alarm rate intensity samples, and the statistical model is built using the 75% remaining low-intensity samples. Pf . CA-CFAR, LN-CFAR, K-CFAR, and 2DLN-CFAR use all of the samples for statistical modeling, However, the proposed TS-2DLNCFAR detector can preserve 97% of the real clutter while so the statistical models are quite inaccurate asstatistical a resultmodel of the high-intensity outliers’ contamination. eliminating the high-intensity outliers, so the is more precise than that of TS-CFAR. As a consequence, the PD degrades. Both TS-CFAR andunder the proposed TS-2DLNCFAR apply clutter TS-2DLNCFAR acquires the highest target detection rate the same observed false alarm rate. truncation firstly, so the statistical models established using the truncated clutter are more accurate than those without clutter truncation. TS-CFAR discards 25% of the high-intensity samples, and the statistical model is built using the 75% remaining low-intensity samples. However, the proposed TS-2DLNCFAR detector can preserve 97% of the real clutter while eliminating the high-intensity outliers, so the statistical model is more precise than that of TS-CFAR. TS-2DLNCFAR acquires the highest target detection rate under the same observed false alarm rate.

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Figure15. 15.ROC ROCcurve curvecomparative comparativeanalysis: analysis:the theblue bluedashed, dashed,the thegreen greendotted, dotted,the theblack blackdash-dotted, dash-dotted, Figure thepink pinkdashed, dashed,the thecyan cyandash-dotted, dash-dotted,and andthe thered reddash-dotted dash-dottedare arethe theROC ROCcurves curvesof ofCA-CFAR, CA-CFAR, the LN-CFAR,K-CFAR, K-CFAR,2DLN-CFAR, 2DLN-CFAR,TS-CFAR, TS-CFAR,and andthe theproposed proposedTS-2DLNCFAR TS-2DLNCFARwith witha a3 3××3 3test test LN-CFAR, window,respectively. respectively. window,

Conclusions 5.5.Conclusions correlation-basedjoint jointCFAR CFARdetector detectorusing usingadaptively-truncated adaptively-truncatedstatistics statisticsininlog-normal log-normal AAcorrelation-based clutterisisproposed proposedininthis thispaper. paper.The TheTS-2DLNCFAR TS-2DLNCFARdetector detectorexploits exploitsthe thegray grayintensity intensitycorrelation correlation clutter information in ship targets and the clutter, and 2DLN distribution is built as the JPDF model the information in ship targets and the clutter, and 2DLN distribution is built as the JPDF model ofofthe seaclutter. clutter.The Thestatistical statisticalmodel modelisisaccurately accuratelyestablished establishedthrough throughan anadaptive adaptivethreshold-based threshold-basedclutter clutter sea truncation in the background window. Compared with traditional CFAR detectors, the statistical truncation in the background window. Compared with traditional CFAR detectors, the statistical modelisismore moreaccurate, accurate,and andititacquires acquiresaahigher higherPD PDininmultiple multipletarget targetsituations, situations,such suchasascrowded crowded model harborsand andbusy busyshipping shippinglanes. lanes. Furthermore, Furthermore, the the FAR FAR isislower lowercompared comparedwith withother otherdetectors, detectors, harbors which has a great application value. which has a great application value. Acknowledgments:This Thiswork work was supported in part byNational the National Natural Science Foundation ofunder China Acknowledgments: was supported in part by the Natural Science Foundation of China grant Nos. 61371154, 61271381, and 61503111, by the Natural ScienceScience Foundation of Anhui under grant under grant Nos. 61371154, 61271381, and 61503111, by the Natural Foundation of Province Anhui Province under 1608085QF142, by the Fundamental Research Funds for the Central grant Nos. 2015HGBZ0106 grant 1608085QF142, by the Fundamental Research Funds forUniversities the Centralunder Universities under grant Nos. and 2015HGQC0005, and the China Postdoctoral Science Foundation under grant No. 2016M592045. The authors 2015HGBZ0106 and 2015HGQC0005, and the China Postdoctoral Science Foundation under grant thank the funds for providing financial and other supports for the research work. The authors would also likeNo. to 2016M592045. The authors thank the funds for providing financial and other supports for the research work. thank the editor, the associate editor, and the anonymous reviewers for their constructive work that significantly The authors would like to thank the editor, the associate editor, and the anonymous reviewers for their elevate the content of also this paper. constructive work that significantly elevate the content of this paper. Xuezhi Yang conceived and designed the CFAR detection method; Author Contributions: Jiaqiu Ai and Xuezhi Yang gave valuable suggestions on the revision of the paper; Jiaqiu Ai and Fang Zhou performed the Author Contributions: Jiaqiu Ai and Xuezhi Dong Yang conceived designed materials; the CFAR Jiaqiu detection method; experiments and analyzed the data; Zhangyu and He Yanand contributed Ai and FangXuezhi Zhou Yang gave valuable suggestions on the revision of the paper; Jiaqiu Ai and Fang Zhou performed the wrote the paper, Lu Jia helped improve the English expression. experiments and analyzed the data; Zhangyu Dong and He Yan contributed materials; Jiaqiu Ai and Fang Zhou Conflicts of Interest: The authors declare no conflict of interest. wrote the paper, Lu Jia helped improve the English expression.

References Conflicts of Interest: The authors declare no conflict of interest. 1.

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