Marine target detection in quad-pol synthetic aperture radar imagery based on the relative phase of cross-polarized channels

Abstract A focus on marine target detection in noise corrupted fully polarimetric synthetic aperture radar (SAR) is presented. The property of the relative phase between two cross-polarized channels reveals that the relative phases evaluated within sea surface area or noise corrupted area are widely spread phase angle region [ − π , π ] due to decorrelation effect; however, the relative phases are concentrated to zero and ± π for real target and its first-order azimuth ambiguities (FOAAs), respectively. Exploiting this physical behavior, the reciprocal of the mean square value of the relative phase (RMSRP) is defined as a new parameter for target detection, and the experiments based on fully polarimetric Radarsat-2 SAR images show that the strong noise and the FOAAs can be effectively suppressed in RMSRP image. Meanwhile, validity of the new parameter for target detection is also verified by two typical Radarsat-2 SAR images, in which targets’ ambiguities and strong noise are present.


Introduction
Target detection based on synthetic aperture radar (SAR) images has been a hot topic because of its important application in maritime environment monitoring.Since the scattering fields from man-made targets, such as ships and oil platforms, are generally stronger than those from surrounding sea surface, the intensity-based constant false alarm rate (CFAR) algorithms have been widely established to distinguish targets from sea surface. 1-12However, the detection algorithms based on single-channel SAR data are sometimes ineffective due to various factors, such as speckle noise, the ambiguities of targets, and other strong noise induced by some uncertain reasons.Recently, with the availability of polarimetric SAR sensors, the polarimetric scattering behavior of targets can be described by the scattering matrix, through which features relating to both the intensity and the relative phase can be extracted.Recently, many polarimetric detection algorithms using polarimetric information provided by fully polarimetric SAR are successfully exploited for detecting targets, especially marine targets. 7-12In Ref. 12, Novak proposed the polarimetric whitening filter method for target detection.On the other hand, the coherent target decomposition (CTD) theory can also be used to observe ships because the scattering mechanisms of targets are generally different from that of surrounding sea surface.The results in Ref. 13 showed that even in low resolution, SAR imageries marine targets can also be distinguished from sea clutter by CTD theory.Generally, the backscattered field from sea surface is dominated by Bragg scattering with low entropy value.However, owing to the complex metallic structures of man-made targets, the scattering field from a man-made target always contains complex scattering mechanisms with higher entropy value.In Refs.14 and 15, based on CTD theory, polarimetric SAR images were used to detect ships exploring entropy values.Note that the effectiveness of the entropy-based detector decreases with increasing wind speed because the scattering field from breaking waves also contains complex scattering mechanisms with higher entropy value.Although the methods mentioned above have been widely used to detect targets in SAR images, the strong noises induced by ambiguities and so on, which are often mistaken as real targets and cause false alarms, cannot be effectively removed.
In Ref. 16, the eigenvalues of the coherency scattering matrix are used to distinguish ambiguities from real targets.However, the method in Ref. 16 will no longer perform well in the case of strong depolarized scattering.In Ref. 17, Liu and Gierull found that in HV þ VH image, the scattering fields of azimuth ambiguities can be suppressed effectively because the HV channel data of the first-order azimuth ambiguities (FOAAs) are approximately equal to VH channel in magnitude but shifted about AEπ in phase.In Ref. 18, based on the intensity of HV þ VH image (it is called as ambiguity free image HV free by Velotto), a new parameter γ, which is a simple combination of slope and departure from the uniform distribution of the phase parameters in GK distribution, is proposed for target detection (refer to Ref. 18 for detail).Velotto et al. pointed out that γ is always smaller than 10 for real targets but larger than 10 for sea surface and ambiguities.The methods proposed in Refs.17 and 18 are applicable to detect targets effectively in highquality SAR images, by this I mean the SAR imageries without exotic noises.Nevertheless, besides ambiguities, many SAR images have also been corrupted by other strong noise induced by uncertain reasons.For the case of the poor-quality SAR images, methods of Liu and Velotto will be no longer in validity.
This paper mainly focuses on detection of azimuth ambiguities in noise severely corrupted fully polarimetric SAR images.We define reciprocal of the mean square value of the relative phase (RMSRP) as a new indicator of marine targets considering the different behaviors of phase difference over real targets and FOAAs.Based on the central limit theorem, we find that the mean value of RMSRP estimated through a 11 × 11 spatially moving window satisfies the Gaussian distribution well.The theoretical distribution of RMSRP is derived and in terms of this, a RMSRP-based CFAR algorithm is established for marine target detection.The experiment results using Radarsat-2 imageries acquired in fine quad-polarization mode are promising, demonstrating that our detection algorithm is not only robust for removal of azimuth ambiguities in SAR images but also is able to suppress noise induced by unknown reasons.This paper is organized as follows.In Sec. 2, the statistic properties of the relative phase and RMSRP are discussed, and the probability density function (PDF) of RMSRP for surrounding sea surface is derived.Section 3 addresses the RMSRP-based CFAR algorithm.Experimental results are presented in Sec. 4, whereas conclusions are given in Sec. 5.

Definition of the New Parameter RMSRP
In this work, the relative phase is estimated by where S HV and S VH denote the single-look complex (SLC), HV and VH scattering amplitudes, and L represents the look-number.
For convenience, the new parameter RMSRP is represented by symbol Θ, and it is defined as where ψ ¼ φ 2 denotes the mean value of φ 2 within a 11 × 11 spatial window.From Eq. ( 2), one can easily conclude that (1) the narrower the PDF of φ, the higher the value of Θ is, and vice versa, and (2) the closer is the mean value of the relative phase from zero, the higher is the value of Θ, and vice versa.

For Real Targets and Its FOAAs
Azimuth ambiguities in SAR images are caused by the discrete sampling of the Doppler signal at finite intervals of the pulse repetition frequency (PRF).The Doppler frequencies higher than PRF would appear as aliased, folded into the azimuth spectrum.Azimuth ambiguities occur at fixed along-track repeat positions with respect to the position of the actual target, i.e., Ref. 19: where x 0 denotes the position of actual target, n ¼ 0; AE1; AE2; • • • is the ambiguity index, λ and R 0 denote the radar wavelength and the slant range, respectively.V is the relative speed between radar and target.For RS-2 data applied in this work, the theoretical distance between the FOAAs and the target is about 4.1 to ∼4.36 km depending on the range position.
For fully polarimetric SAR systems, the horizontal (H) and vertical (V) pulses are transmitted alternately.Thus, the time interval between HV and VH signals is 1/2PRF.If the HV ambiguous response occurs at position x ¼ x 0 þ nðλR 0 ∕2VÞPRF, then the corresponding VH ambiguous would occur at The azimuth phase history for a target positioned at x 0 can be represented by Substituting Eqs. ( 3) and ( 4) into Eq.( 5), the relative phase between the ambiguous HV and VH returns is obtained as For real targets, the reciprocity condition, i.e., S VH ¼ S HV , should be satisfied.However, there exists an additional phase shift ð2π∕λR 0 ÞðV 2 ∕4PRF 2 Þ in Eq. ( 6), which can be removed by multiplying a complex number during the resampling processes so that Eq. ( 6) is simplified to φ ¼ nπ.Then the relative phase between two cross-polarized channels is φ ¼ 0 for real target AEπ for FOAAs :

For Sea Surface and the Strong Noise
In SAR images, for sea surface and the strong noise, the relative phase between two cross-polarized channels has been widely spread in angle region ½−π; π due to decorrelation effect.The histograms of φ evaluated by SLC quad-pol RS-2 SAR data are illustrated in Fig. 1.It is clearly shown that the relative phase is equal to 0 rad for real target, and the PDF is very narrow.Just as discussed in Sec.2.1, the PDF for FOAAs is distributed around AEπ, but it has been spread because the field intensities of ambiguities are generally much lower than real target and can be easily affected by sea clutter.Figure 1 also shows that the relative phases for sea surface and strong noise are widely spread in angle region ½−π; π due to decorrelation effect.In order to detect target by RMSRP-based CFAR algorithm, the "prior probability" of Θ should be obtained first.In Refs.20 and 21, the PDF of the relative phase φ has been derived by Lee as where FðL; 1; 1∕2; β 2 Þ is a Gauss hypergeometric function, β ¼ jρj cosðφ − hφiÞ, the correlation coefficient jρj and the mean phase hφi are related to the measured data by Using Eq. ( 8), the PDF of φ 2 is derived as Based on the central limit theorem, if the dimension number of a moving window is large enough, the PDF of ψ (i.e., the mean value of φ 2 within the moving window) can be described approximately by a Gaussian distribution where μ ψ and σ 2 ψ denote the mean value and the mean square deviation of ψ, respectively.Then, using the identity equation PðψÞjdψj ¼ PðΘÞjdΘj, the PDF of Θ is obtained Using Eqs. ( 10) and ( 12), the mean values of Θ for different look numbers are evaluated, and the curves are plot in Fig. 2. Just as shown in this figure, the value of Θ increases with the increase of look number and correlation coefficient.And the effect of look number is more remarkable when the correlation coefficient is larger.This property implies that multilook processing would improve the ability of Θ for target detection because the correlation coefficients for real targets are always larger than those for surrounding sea surface.However, it should be pointed out that the multilook processing would reduce the spatial resolution.On the other hand, to ensure the applicability of the central limit theorem, the dimension of the moving window, in which the mean value of φ 2 is evaluated, is set to be 11 × 11 pixels.In this work, a data set that contains six Radarsat-2 SAR images acquired in fine quad-polarization mode are processed to show the effectiveness of the theoretical PDF.The detailed descriptions of the images are given in Table 1.The comparisons in Fig. 3 illustrate that the theoretical PDFs match the histograms well.

Θ-based CFAR Target Detector
Here, a Θ-based CFAR algorithm is established for marine target detection.The detection threshold ξ is determined by the following integration: where η is the given false alarm.And erfð•Þ denotes the error function.Using Eq. ( 13), the relation between the false alarm rate η and the detection threshold ξ is derived as where erfinvð•Þ denotes the inverse error function.
Based on the analysis above, the following rule is used to detect targets, i.e.,

Experimental Results
In this section, three meaningful Radarsat-2 SAR imageries (namely Image RS_V, Image RS_VI and Image RS_VII in Table 1), in which targets, azimuth ambiguities, and strong noise are simultaneously present, have been selected to demonstrate the effectiveness of the Θ-based target detector.In the following discussions, the false alarm rate η is set to be 10 −5 .First, the Θ-based target detector is tested to remove azimuth ambiguities.Figure 4 shows the SAR image of the Dongsha Island acquired at 10:12 (UTC) on August 8, 2012 (namley Image RS_VII in Table 1).From Fig. 4, we can find that the first-order azimuth ambiguity of the Dongsha Island can be seen in jHHj and jHVj images.In jHV þ VHj image (i.e., the so called HV free image in Ref. 18), the intensity of the azimuth ambiguity has been suppressed due to its special phase difference.From Fig. 4(d), we can find that the value of Θ (i.e., RMSRP) for target/ azimuth ambiguity is higher/lower than the surrounding sea surface.Thus, the parameter Θ can also be used to remove the azimuth ambiguities.Table 2 The information of the targets in Fig. 5. given in Table 2.This ground truth is consistent with the detection results, further supporting our proposed detector.The largest ship in Fig. 5 is T18, with 294 m in length and 32 m in width.
There do exist two odd targets circled by red rectangle in Fig. 5(f), and no AIS information indicates these targets.
Another typical example of target detection in a noise-corrupted SAR imagery is presented in Fig. 6.The SAR image in Fig. 6 was acquired at 09:39 (UTC) on July 13, 2010, in the East China Sea.And the center longitude and latitude coordinates are 122°34′54′′E and 31°11′43′′N, respectively.Besides real targets, some filaments could be seen in Figs.6(a)-6(c), and we have no idea about the origin of these odd noise.Figure 6(f) demonstrates promising detection result with threshold of 0.67.It is exciting to find that the strong noise has been suppressed in the RMSRP image, highlighting the visually inspected ships.This imagery provides further evidence to the applicability of our proposed algorithm.To present a quantitative description about the reduction degree of noise, we introduce the standard deviation of jHHj, jHVj, jHV þ VHj, and RMSRP over the noise-corrupted areas to indicate this improvement.We select two areas in Fig. 5(d) marked as AR1, AR2, and one area AR3 in Fig. 6(b) to demonstrate the improvement of RMSRP in suppressing noise.The detailed estimates for different parameters are given in Table 3, and it is evident that the noise is primarily reduced by RMSRP while others do not exhibit such capability.It also should be noted that the standard deviation of jHV þ VHj is always the largest value, by this I mean that noise presents the highest variability in jHV þ VHj images.

Conclusions
In this paper, the RMSRP between cross-polarized channels is proposed as a new promising indicator for SAR target detection at sea.Meanwhile, an analytical form of the PDF for RMSRP was derived, and the comparisons between the histograms of the sea clutter and theoretical PDF show the correctness of the statistic model.Based on the statistic model, a RMSRPbased CFAR algorithm is developed to detect targets in noise corrupted SAR images.From the tests over quad-pol RS-2 SAR images, we find that not only the azimuth ambiguities but also strong noise can be reduced successfully by the RMSRP-based algorithm.Standard deviation is introduced to indicate the quantitative improvement in suppressing noise.The experiment results certify that RMSRP is a promising indicator for Pol-SAR target detection purpose, particularly when pol-SAR images have been corrupted by strong noise and azimuth ambiguities.This proposed algorithm would be helpful in detecting targets in SAR imageries and further applying to coastal management.
The information for T 27 and T 28 are achieved from ENC (electronic navigation chart) C1311700.No AIS information are available for T10 and T26.The information for the other targets is all obtained by AIS (automatic identification system).

Table 3
Standard deviation over noise-corrupted areas.