Ship Detection in PolSAR Images Based on a Modified Polarimetric Notch Filter

Abstract

Ship detection based on synthetic aperture radar (SAR) imagery is one of the key applications for maritime security. Compared with single-channel SAR images, polarimetric SAR (PolSAR) data contains the fully-polarized information, which better facilitates better discriminating between targets, sea clutter, and interference. Therefore, many ship detection methods based on the polarimetric scattering mechanism have been studied. To deal with the false alarms caused by the existence of ghost targets, resulting from azimuth ambiguities and interference from side lobes, a modified polarimetric notch filter (PNF) is proposed for PolSAR ship detection. In the proposed method, the third eigenvalue obtained by the eigenvalue–eigenvector decomposition of the polarimetric covariance matrix is utilized to construct a new feature vector. Then, the target power can be computed to construct the modified PNF detector. On the one hand, the detection rate of ship targets can be enhanced by target-to-clutter contrast. On the other hand, false alarms resulting from azimuth ambiguities and side lobes can be reduced to an extent. Experimental results based on three C-band AIRSAR PolSAR datasets demonstrated the capability of the proposed PNF detector to improve detection performance while reducing false alarms. To be specific, the figure of merit (FoM) of the proposed method is the highest among comparative approaches with results of 80%, 100%, and 100% for the tested datasets, respectively.

1. Introduction

With the rapid development of synthetic aperture radar (SAR) imaging algorithms and systems, many SAR sensors with higher resolution, multiple imaging modes, and the capability for multi-polarization have been developed to provide abundant imagery in both civilian and military applications. Among the applications, marine target detection based on SAR images has been a hot research topic in recent decades.

Taking a single channel from multi-channel full-polarized SAR images, ship detection can be conducted with typical approaches designed for single-polarized SAR images. In [1], Marino et al. utilized the cross-polarization channel HV image to detect ships. Up to now, many approaches have been proposed for single-polarized SAR imagery, including the following: the conventional constant false alarm rate (CFAR) detector and its different versions [2,3,4,5,6], saliency detectors [7,8], and deep learning networks [9,10,11], etc. To perform ship detection using SAR images, many methods depend heavily on the intensity contrast between man-made metallic targets, sea or ground clutter, and other interference. However, sometimes the intensity difference between targets and background clutter is too minor for good detection [5]. For instance, when applying a pixel-level CFAR detector [2,3,4] to high-resolution SAR images performance may deteriorate, since there is more severe speckle noise and the intensity difference between ship and clutter decreases. To deal with this issue, many approaches have been presented, including clutter censoring schemes [3,4], clutter truncation methods [5], and superpixel-level CFAR detectors [5,6], etc.

Even though improved performance can be obtained, there unavoidably exist false alarms caused by ghost targets or interference. One of the typical ghost targets is the azimuth ambiguity [12] caused by the aliased Doppler phase history during the SAR imaging process. Since the main source of azimuth ambiguities comes from metallic structures (such as ships) with great backscattering responses, the targets are often similar in intensity and size, making it difficult to remove corresponding false alarms. Several removal methods [12,13,14] for azimuth ambiguities have been proposed for the imaging process or in preprocessing before target detection. A band-pass Wiener filter [13] was designed to select a non-aliased spectrum with space-adaptivity for azimuth ambiguity removal in complex-valued SAR images, thereby resulting in ambiguity-free images. In [14], a mathematical model was constructed for strip map SAR images, and azimuth suppression performed for the original SAR echo. However, most methods are based on the analysis of complex-valued SAR data. In practical applications, the majority of SAR datasets for target detection or visual interpretation are stored with real-valued amplitude or intensity. Therefore, the aforementioned methods cannot be properly adopted for SAR amplitude images.

Since the technique of multi-polarization provides more physical mechanism-related information to discriminate targets from sea clutter, polarimetric SAR (PolSAR) images are widely used in the application of target detection to improve ship detection performance. According to [15], there are five typical types of ship detection methods for PolSAR data involving pixel-level detectors and patch-level detectors. To be specific, the main schemes are the following: the composition of independent polarized channels, polarization optimization, polarimetric scattering characteristics, and machine learning or deep learning. One type of pixel-level approach depends on a combination of multi-polarized scattering information embedded in the Sinclair matrix of the second-order covariance matrix, and includes the following: the SPAN detector [16], using total polarimetric power; the polarimetric whitening filter (PWF) detector [17,18], providing good speckle suppression; the polarimetric notch filter (PNF) detector [19] and its varied versions [15], Without prior knowledge of targets; the PWF [17,18], designed to suppress the speckle influence for target detection. In theory, the performance of PWF can be comparable to that of the optimal polarimetric detector (OPD) [20], which was derived from the likelihood ratio test for Wishart-distributed targets and clutter. A saliency detector, based on a similarity test and offering speckle-free PolSAR images, was proposed in [21]. In [22], Zhang et al. introduced neighborhood polarimetric covariance matrices into the superpixel-based PWF detector, which improved the detection performance of PWF. Recently, in [23], combining sub-aperture decomposition techniques, a sub-PWF detector was proposed to simultaneously enhance the coherence of sea clutter and ships. To be specific, the geometrical perturbation PNF (GP-PNF) satisfies the assumption that the sea clutter in a local region is a Bragg surface with homogeneous polarimetric characteristics, while the target behaves differently [19]. Based on the designed feature partial scattering vector, the PNF detector can be defined to minimize the power of sea clutter.

Another type of PolSAR target detection depends on target decomposition techniques, such as eigenvalue–eigenvector decomposition [24,25], H-$\alpha$ decomposition [26], the Freeman decomposition with three components [27], and the four-component Yamaguchi decomposition and its generalized version [28,29]. On the basis of target decomposition, many effective features can be further extracted, including the entropy [26], generalized polarization relative entropy [30], polarimetric cross entropy, and eigenvalues, etc. For instance, based on eigenvalue–eigenvector decomposition, eigenvalue ${\lambda }_3$, was applied in [31] for azimuth ambiguity removal when detecting ships using PolSAR images. However, the performance of ${\lambda }_3$ may be restricted for ship targets with simple structures [32]. The decomposition of the polarimetric covariance difference matrix (PCDM) was used by Zhang et al. [33] to compute the pedestal ship height (PSH) with eigenvalues ($PSH=\frac{\left|{\lambda }_3\right|}{\left|{\lambda }_1\right|+\left|{\lambda }_2\right|}$), so as to reduce false alarms generated by ghosts of real targets due to the phenomenon of azimuth ambiguity. Other approaches also achieved the purpose of azimuth ambiguity removal. In [34], ship targets and ambiguities were discriminated by using L-band PolSAR datasets. In our previous work [32], the unsupervised classification method, based on the ${\mathcal{G}}_p^0$ mixture model, was utilized to discriminate targets from clutter and azimuth ambiguities.

Other detectors, such as the following are also studied for target detection in PolSAR detection: CFAR detector [35], SIFT-like keypoint detector [36], Wishart classifier [37], and deep learning networks [38,39,40], etc. Specifically, the clutter truncation scheme was extended to the CFAR detector for PolSAR imagery [35], providing a truncated version of the Gamma and Wishart model for PWF samples. In [36], the PolSAR–Harris function was constructed, based on gradient defined with Riemannian distance, and then target keypoints are detected and used to construct the detection statistics. However, the performance of the SIFT-like keypoint detector cannot be ensured under high seas conditions or more complex environments. Taking advantage of deep learning techniques, several convolutional neural networks (CNNs) [38,39,40] have been applied to PolSAR imagery. A lightweight patch-to-pixel CNN (named P2P-CNN) was proposed in [38], referring to a residual network structure which can be used for multi-class detection and one-class ship detection. Sparse representation was combined to the CNN architecture in [40] to combine the polarimetric information of the target with the spatial information. However, since the open and standard PolSAR target detection datasets are unreleased, research on CNN methods driven by PolSAR data for target detection is limited.

To provide a better solution to ship target detection in PolSAR imagery, while removing azimuth ambiguities, the third eigenvalue ${\lambda }_3$, computed by eigenvalue–eigenvector decomposition, was utilized in the paper presented to construct a new feature vector for a modified NPNF detector. The main contributions of the proposed method can be summarized as follows. First, taking advantage of the eigenvalue–eigenvector decomposition result, a modified ship detector is proposed under the new framework of a polarimetric notch filter. Second, the proposed method is verified against fully-polarized C-band AIRSAR data, capable of azimuth ambiguity removal. False alarms generated by interfering side lobes can be reduced by the proposed method.

The rest of the paper has the following structure. First, several related works are introduced in Section 2. Then, the theory of polarization and the principle of PNF detectors are introduced in Section 3. Section 4 introduces the detailed information of the proposed method. The next section provides corresponding experimental settings and comparative results on the test AIRSAR datasets. Finally, Section 6 provides the conclusion.

2. Related Works

The original PNF detector [19] was based on the idea of geometrical perturbation. The designed partial scattering vector of the PNF detector minimizes the power of sea clutter [19]. The corresponding ${\chi }^2$ statistical tests and the CFAR detector for the PNF were analyzed in [41,42], respectively. Furthermore, the original PNF was successively extended in its target detection task with the ALOS-PALSAR [43], TanDEM-X Data [44] and compact polarimetric SAR data [45], successively. In [15], a new form of PNF detector, denoted as NPNF, was proposed, based on single target vectors, which provided better detection performance than the original PNF in [19]. Recently, based on quadratic optimization, a general framework was constructed for polarimetric detectors, including the SPAN detector, PWF detector, and NPNF detector, in [46]. According to [46], the issue with PNF lies in its suppression of both clutter and targets. Although the PNF in [19] can detect real targets, its detection results unavoidably contain false alarms resulting from azimuth ambiguities, since the feature vector of PNF contains the characteristics of azimuth ambiguities [47]. To remove ambiguities, the eigenvalue ${\lambda }_3$ was applied in [31] for azimuth ambiguity removal when detecting ships from PolSAR images. However, only using ${\lambda }_3$ cannot guarantee good performance for ship targets with simple structures [32]. Based on the decomposition of PCDM, the PSH feature was computed with eigenvalues in [33]. The latter was applied by Zhang et al. to modify the original GP-PNF detector and to design a new PNF detector in [47], with the goal of azimuth ambiguity removal in PolSAR images. However, the performance of PSH may miss detection of large targets or small targets overlapped with ambiguities [33]. Therefore, taking advantage of the capability of ${\lambda }_3$ in removing azimuth ambiguities and the excellent framework of NPNF, a modified detector is designed in this paper to improve target detection performance in PolSAR images.

3. Theoretical Background of the Proposed Method

3.1. Polarimetric Theory

Based on the polarization mechanism, targets can be fully described with the Sinclair matrix $\mathit{S}$ consisting of four backscattering coefficients, which can be denoted as follows:

$$\begin{array}{c}\hfill \mathit{S}=\left[\begin{array}{cc}{S}_{HH}& S_{HV}\\ S_{VH}& S_{VV}\end{array}\right],\end{array}$$

(1)

where the subscripts V and H represent polarization modes in the vertical and horizontal directions, respectively. The different composite patterns of H and V can denote polarizations with different transmitting and receiving states. If the monostatic reciprocity assumption is satisfied, the symmetric receiving backscattering echo can be obtained, i.e., $S_{HV}=S_{VH}$. Therefore, $\mathit{S}$ can be simplified as a scattering vector $\mathit{k}$ under the Lexicographic matrix basis set, yielding

$$\begin{array}{c}\hfill \mathit{k}={\left[k_1,k_2,k_3\right]}^T={\left[S_{HH},\sqrt{2}{S}_{HV},S_{VV}\right]}^T,\end{array}$$

(2)

where ${[·]}^T$ denotes the transpose operation. To utilize the abundant information contained in the PolSAR data, the scattering vector $\mathit{k}$ can be adopted to deduce the covariance matrix using $\mathit{C}=〈\mathit{k}·{\mathit{k}}^H〉$, resulting in

$$\begin{array}{c}\hfill \begin{array}{c}\mathit{C}=\left[\begin{array}{ccc}〈{\left|S_{HH}\right|}^2〉& \sqrt{2}〈S_{HH}{S}_{HV}^{\ast }〉& 〈S_{HH}{S}_{VV}^{\ast }〉\\ \sqrt{2}〈S_{HV}{S}_{HH}^{\ast }〉& 2〈{\left|S_{HV}\right|}^2〉& \sqrt{2}〈S_{HV}{S}_{VV}^{\ast }〉\\ 〈S_{VV}{S}_{HH}^{\ast }〉& \sqrt{2}〈S_{VV}{S}_{HV}^{\ast }〉& 〈{\left|S_{VV}\right|}^2〉\end{array}\right]=\left[\begin{array}{ccc}{C}_{11}& C_{12}& C_{13}\\ C_{21}& C_{22}& C_{23}\\ C_{31}& C_{32}& C_{33}\end{array}\right]\end{array},\end{array}$$

(3)

where ${[·]}^H$ is the conjugate transpose operation, ${[·]}^{\ast }$ represents the complex conjugate, $\left|·\right|$ denotes the magnitude, and $〈·〉$ conducts the spatial averaging operation.

3.2. Theory of Polarimetric Notch Filter (PNF)

3.2.1. The Original PNF

With the partial target mechanism, the feature partial scattering vector can be denoted as the following six-dimensional vector, according to the covariance matrix of PolSAR data.

$$\begin{array}{c}\mathit{t}=\mathrm{tr}\left(\mathit{C}{\Psi }_3\right)={\left[t_1,t_2,t_3,t_4,t_5,t_6\right]}^T\hfill \\ ={\left[〈{\left|k_1\right|}^2〉,〈{\left|k_2\right|}^2〉,〈{\left|k_3\right|}^2〉,〈k_1^{\ast }{k}_2〉〈k_1^{\ast }{k}_3〉〈k_2^{\ast }{k}_3〉\right]}^T\hfill \\ ={\left[C_{11},C_{22},C_{33},C_{12},C_{13},C_{23}\right]}^T,\hfill \end{array}$$

(4)

where $\mathrm{tr}\left(·\right)$ computes the matrix trace. Under the Hermitian inner product, the complete set of $3\times 3$ basis matrices ${\Psi }_3$ can be obtained.

Applying the geometrical perturbation (GP) to PNF in PolSAR data, Marino et al. proposed the GP-PNF in [19] for the purpose of ship detection. For the fully-polarized SAR, the formation of the GP-PNF detector can be denoted as follows:

$$\begin{array}{c}\hfill \gamma =\frac{1}{\sqrt{1+\frac{\mathrm{RedR}}{{\mathit{t}}^{\ast T}\mathit{t}-{\left|{\mathit{t}}^{\ast T}{\widehat{\mathit{t}}}_{sea}\right|}^2}}}=\frac{1}{\sqrt{1+\frac{\mathrm{RedR}}{P_T}}}>T,\end{array}$$

(5)

where $\mathrm{RedR}$ represents the reduction ratio, $\mathit{t}$ denotes the six-dimensional partial feature vector of the target, and ${\widehat{\mathit{t}}}_{sea}={\mathit{t}}_{sea}/\phantom{{\mathit{t}}_{sea}∥{\mathit{t}}_{sea}∥}∥{\mathit{t}}_{sea}∥$ describes the six-dimensional unitary partial feature vector of sea clutter. The value $P_T$ is the power of the target. Specifically, when ship targets exist, the value of $1/\phantom{1P_T}{P}_T$ is close to 0, yielding an approximate value of $\gamma$ to be 1. On the contrary, if there is only sea, the $\gamma$ is close to 0.

It is noted that the $\mathrm{RedR}$ and threshold T together define the ship detector. To be specific, the $\mathrm{RedR}$ can be set by considering the minimum target of interest $P_T^{min}$, denoted as follows.

$$\begin{array}{c}\hfill \mathrm{RedR}={\mathrm{P}}_{\mathrm{T}}^{min}\left(\frac{1}{{\mathrm{T}}^2}-1\right).\end{array}$$

(6)

3.2.2. New PNF (NPNF)

With the original version of PNF, in [19], in mind, the feature scattering vector is constructed for partial targets, assigning identical importance to the six elements extracted from the covariance matrix. To concentrate more on the difference between the physical scattering mechanism of ship targets and that of background clutter, Liu et al. introduced a new PNF structure (denoted as NPNF), in [15], which considers the situation of single targets. In the NPNF detector, the power of the target is evaluated in terms of the trace of the covariance matrix, which can be expressed by the following formulation:

$$\begin{array}{c}\hfill P_T={\mathit{k}}^H\mathit{k}-{\mathit{k}}^H\left({\widehat{\mathit{k}}}_{sea}{{\widehat{\mathit{k}}}^H}_{sea}\right)\mathit{k}={\mathit{k}}^H\mathit{k}-{\mathit{k}}^H{\widehat{\mathit{C}}}_{sea}\mathit{k}={\mathit{k}}^H\left(\mathit{I}-{\widehat{\mathit{C}}}_{sea}\right)\mathit{k},\end{array}$$

(7)

where $\mathit{I}$ denotes the identity matrix, and ${\widehat{\mathit{C}}}_{sea}$ represents the normalized covariance matrix [15]. For partial targets, to reduce the influence of speckle noise on the detection result, the Boxcar filter is adopted to conduct averaging. Thus, $P_T$ can be expressed as

$$\begin{array}{c}\hfill P_T=\frac{1}{L}\sum _{i=1}^L{\mathit{k}}_i^H\left(\mathit{I}-{\widehat{\mathit{C}}}_{sea}\right){\mathit{k}}_i=\mathrm{tr}\left(\left[\mathit{I}-{\widehat{\mathit{C}}}_{sea}\right]\mathit{C}\right),\end{array}$$

(8)

where ${\widehat{\mathit{C}}}_{sea}=〈{\widehat{\mathit{k}}}_{sea}{{\widehat{\mathit{k}}}^H}_{sea}〉={\mathit{C}}_{sea}/\mathrm{tr}\left({\mathit{C}}_{sea}\right)$ denotes a $6\times 6$ positive semidefinite Hermite matrix for the NPNF. Then, $\left(\mathit{I}-{\widehat{\mathit{C}}}_{sea}\right)$ is found to be an orthogonal projection matrix.

4. Methodology

4.1. Eigenvalue Decomposition

To remove false targets from detection results, the eigenvalue–eigenvector decomposition is applied to extract distinguishing features for targets and azimuth ambiguities. To be specific, the ${\lambda }_3$ is utilized to modify the PNF detector for the purpose of improving target detection performance. According to [24,25,26], the coherency matrix $〈\mathit{T}〉$ can be decomposed into three independent components (denoted by ${\mathit{T}}_i$) of rank 1, as follows:

$$\begin{array}{c}\hfill 〈\left[\mathit{T}\right]〉=\sum _{i=1}^3{\lambda }_i\left[{\mathit{T}}_i\right],\end{array}$$

(9)

where the relationship for the three positive real eigenvalues holds, i.e., ${\lambda }_1\ge {\lambda }_2\ge {\lambda }_3$. According to [24,25], the eigenvalues are roll-invariant and basis-invariant. The covariance matrix $\mathit{C}$ should be transformed to the coherency matrix by the following relationship:

$$\begin{array}{c}\hfill \mathit{T}={\mathit{U}}_{3(L\to P)}{\mathit{CU}}_{3(L\to P)}^{-1},\end{array}$$

(10)

where ${\mathit{U}}_{3(L\to P)}$ is a unitary matrix.

$$\begin{array}{c}\hfill {\mathit{U}}_{3(L\to P)}=\frac{1}{\sqrt{2}}\left[\begin{array}{ccc}1& 0& 1\\ 1& 0& -1\\ 0& \sqrt{2}& 0\end{array}\right].\end{array}$$

(11)

If only ${\lambda }_1$ is non-zero, the coherency matrix relates to pure point targets, such as corner reflectors. If the three eigenvalues are identical to each other, the coherency matrix represents a random combination of the three scattering mechanisms [25]. Ship targets can be regarded as a mixture of three scattering mechanisms, including single-bounced, double-bounced, and depolarized mechanisms, among which the former two may lead to azimuth ambiguities. Therefore, the weight of depolarized scattering vector consisting of azimuth ambiguities should be small, corresponding to a small value of ${\lambda }_3$.

4.2. The Modified NPNF Detector Based on ${\lambda }_3$

Taking the structure of NPNF as the basis, a modified ship target detection method, based on ${\lambda }_3$, is presented, which has the capability of azimuth ambiguity removal. To be specific, a new scattering feature vector $t_{new}$ is constructed by combining the ${\lambda }_3$ with the original scattering feature vector, based on which the target detector is designed.

$$\begin{array}{c}\hfill \begin{array}{c}{\mathit{t}}_{new}={\mathit{C}}_n={[C_{n11},C_{n22},C_{n33},\left|C_{n12}\right|,\left|C_{n13}\right|,\left|C_{n23}\right|]}^T={\lambda }_3\times {[t_1,t_2,t_3,t_4,t_5,t_6]}^T\hfill \\ ={\lambda }_3\times {\left[〈{\left|k_1\right|}^2〉,〈{\left|k_2\right|}^2〉,〈{\left|k_3\right|}^2〉,〈k_1^{\ast }{k}_2〉〈k_1^{\ast }{k}_3〉〈k_2^{\ast }{k}_3〉\right]}^T\hfill \\ ={\lambda }_3\times {\left[C_{11},C_{22},C_{33},C_{12},C_{13},C_{23}\right]}^T.\hfill \end{array}\end{array}$$

(12)

Taking ${\lambda }_3$ as a multiplication factor of the original scattering vector, an enhanced target-to-clutter ratio can be achieved. The magnitude of ghost targets caused by azimuth ambiguities is weakened, facilitating the removal of extra false alarms and improving detection accuracy.

Substituting the new feature vector ${\mathit{C}}_n={\left(C{}_n{}_{\mathrm{ij}}\right)}_{3\times 3}$ and ${\widehat{\mathit{C}}}_{sea\_n}={\left(C{}_{sea\_n}{}_{\mathrm{ij}}\right)}_{3\times 3}$ into the formulation of $P_T$ in Equation (8):

$$\begin{array}{c}\hfill \begin{array}{c}{P}_{T-NPNF}=\mathrm{tr}\left(\left[\mathit{I}-{\widehat{\mathit{C}}}_{sea\_n}\right]{\mathit{C}}_{\mathit{n}}\right)\hfill \\ =\frac{1}{C_{sea\_n11}+C_{sea\_n22}+C_{sea\_n33}}\hfill \\ \times [C_{n11}\left(C_{sea\_n11}+C_{sea\_n22}\right)+C_{n22}\left(C_{sea\_n11}+C_{sea\_n33}\right)+C_{n33}\left(C_{sea\_n11}+C_{sea\_n22}\right)\hfill \\ -2\mathrm{Re}\left(C_{n12}{C}_{sea\_n12}^H\right)-2\mathrm{Re}\left(C_{n13}{C}_{sea\_n13}^H\right)-2\mathrm{Re}\left(C_{n23}{C}_{sea\_n23}^H\right)],\hfill \end{array}\end{array}$$

(13)

where $\mathrm{Re}\left(·\right)$ represents the real part of a complex number. Then, the final detector ${\gamma }_{new}$ is constructed with the computed target power $P_{T-NPNF}$ as follows:

$$\begin{array}{c}\hfill {\gamma }_{new}=\frac{1}{\sqrt{1+\frac{\mathrm{RedR}}{P_{T-NPNF}}}}>T.\end{array}$$

(14)

In [19], a typical value of $T=0.98$ is chosen arbitrarily, resulting in an approximate value of $\mathrm{RedR}$ being $2\times {10}^{-3}$. In the proposed method, the same parameters are set.

To provide clear illustration, the whole procedure of the proposed method is presented in Figure 1. Specifically, the main steps are detailed as follows:

Step (1) Input the covariance matrix $\mathit{C}$ of PolSAR data.

Step (2) Perform small window Boxcar filtering to the input $\mathit{C}$ of PolSAR data. In the experiment, a $5\times 5$ Boxcar filtering was adopted.

Step (3) Conduct eigenvalue composition based on the filtered $\mathit{C}$ to obtain the ${\lambda }_3$.

Step (4) Construct the new feature vector $t_{new}$ based on the Equation (12).

Step (5) Perform large-size window Boxcar filtering to the new feature vector $t_{new}$ to obtain the estimated feature vector ${\widehat{\mathit{C}}}_{sea\_n}$ for the clutter region. In the experiment, a $50\times 50$ Boxcar filtering was adopted to extract the ${\widehat{\mathit{C}}}_{sea\_n}$. A small window Boxcar filtering was selected to obtain the feature vector for the pixel to be detected, since $5\times 5$ Boxcar filtering had already been performed in the preprocessing stage.

Step (6) Compute the modified target power based on Equation (13).

Step (7) Construct the new target detector ${\gamma }_{new}$ based on Equation (14) and the pre-set parameters, i.e., the threshold T and the reduction ratio $\mathrm{RedR}$.

Step (8) According to the set threshold T, the detection result $BW$ can be obtained as follows:

$$\begin{array}{c}\hfill BW=\left\{\begin{array}{c}1,{\gamma }_{new}\ge T,\mathrm{target}\mathrm{pixel}\\ 0,{\gamma }_{new}<T,\mathrm{clutter}\mathrm{pixel}\end{array}\right.\end{array}$$

(15)

5. Experiment Results and Analysis

For the purpose of testing the effectiveness of the performance of the proposed method, experiments were conducted with three AIRSAR C-band PolSAR datasets, collected from different Japanese bays. The corresponding information of tested datasets are shown in

Table 1. The tested AIRSAR datasets.

Scene Name	Polarization	Size (Pixels)	Range and Azimuth Pixel Spacing (m)	Collected Area	Collected Time
A	Full polarized	800 × 700	3.33 × 4.63	Kojimawan Bay, Japan	4 October 2000
B	Full polarized	450 × 750	3.33 × 4.63	Tokyo Bay, Japan	2 October 2000
C	Full polarized	600 × 600	3.33 × 4.63	Hiroshima Bay, Japan	4 October 2000

https://vertex.daac.asf.alaska.edu (accessed on 15 March 2023).

. In fact, the original dataset contained both C- and L-band PolSAR images, which were well co-registered. However, we note that azimuth ambiguity only appears in the C-band dataset [32], so the position of azimuth ambiguities can be pointed out by comparing the C- and L-band PolSAR images. In the experiment, the C-band image was adopted to testify to the capability of our method in removing false alarms generated by azimuth ambiguity. Comparisons with four existing methods, the PCDM [33], PWF [18], PNF [19], and NPNF [15], were conducted. The PCDM method was proposed by Zhang et al. [33], wherein eigenvalue–eigenvector decomposition was adopted to compute the $PSH=\frac{\left|{\lambda }_3\right|}{\left|{\lambda }_1\right|+\left|{\lambda }_2\right|}$ feature so as to remove false alarms caused by azimuth ambiguities. The PWF was proposed to suppress the speckle influence on target detection performance [18]. In the experiment, a CFAR detector was employed with the composite image of PWF to obtain detection results. Since the proposed method is based on the idea of PNF, the performances of the original form of the PNF detector, in [19], and the new form of the NPNF detector, in [15], were compared.

To provide quantitative evaluation to the performance of comparative approaches, three assessment merits were introduced, i.e., the detection rate $P_d$, the false alarm rate $P_{fa}$, and the figure of merit (FoM), the definitions of which follow:

$$\begin{array}{c}\hfill \begin{array}{c}{P}_d=\frac{N_{td}}{N_{gt}},\hfill \\ P_{fa}=\frac{N_{fa}}{N_{td}+N_{fa}},\hfill \\ \mathrm{FoM}=\frac{N_{td}}{N_{fa}+N_{gt}},\hfill \end{array}\end{array}$$

(16)

where $N_{td}$, $N_{fa}$ and $N_{gt}$ are the numbers of correctly detected targets, false alarms, and ground-truth targets, respectively.

5.1. Results and Analysis on the First AIRSAR Dataset

In the first experiment, a NASA/JPL AIRSAR PolSAR dataset, collected from the Kojimawan Bay, Japan, was utilized. Since the original dataset was too large, a subimage, cropped to a a size of 800 × 700 pixels, was utilized. First, 9-look multilook processing was conducted to obtain the polarimetric covariance matrix, resulting in a resolution in the range and azimuth directions of about 10 m and 13.9 m, respectively. Figure 2 shows the Pauli RGB image and its grayscale counterpart. The ground-truth location of real targets and ghost ships are marked with yellow and red rectangles, attached with signs “T” and “A”, respectively. It is noted that more than one ghost may exist for a single target. For instance, there were two ghost targets for “T18” in the azimuth direction, denoted by “A18” and “A${18}^{\prime }$”, respectively. Overall, there were, in total, 21 ships and 8 ghost targets in the first PolSAR image. There is a large range of variation in size of targets, which poses great challenge to obtaining a high detection rate. Since ghost targets, caused by azimuth ambiguity, have high scattering intensity, it is difficult to discriminate ghost targets from real ships based on the grayscale intensity information. Furthermore, from visual effects, some small targets (such as “T3”) have lower intensity than the ghost targets.

The comparison of ${\lambda }_3$ with its counterparts ${\lambda }_1$ and ${\lambda }_2$ is provided in Figure 3. The single-bounced (reflected by ${\lambda }_1$) and double-bounced (reflected by ${\lambda }_2$) scattering vectors of targets and that of azimuth ambiguities were similar, shown in Figure 3a,b. However, the depolarized scattering mechanism of targets is different from that of azimuth ambiguities, which can be reflected by ${\lambda }_3$. Specifically, the ${\lambda }_3$ of azimuth ambiguities was significantly lower than that of real targets, which can be observed in Figure 3c. Therefore, the ${\lambda }_3$ information could be used to discriminate between azimuth ambiguities and real ship targets. The ${\lambda }_3$ also performed well when detecting ship targets interfered with by the side lobes, which is validated in the following experimental section.

The corresponding power images before the threshold processing are provided in Figure 4 for the five methods tested. For fair comparison, the magnitude of each power image was normalized into the interval [0, 1]. According to the direct visual effects, the three PNF approaches enhanced the ship targets, while suppressing the sea surface. However, for PNF and NPNF, the azimuth ambiguities were also enhanced. By contrast, taking advantage of ${\lambda }_3$, the power image of the proposed method achieved good performance for azimuth ambiguity removal. Both the PWF detector and the PCDM methods obtained low-contrast power images. However, differing from the PWF result, it can be seen that the azimuth ambiguities were reduced in the PCDM result.

The comparative detection results of the methods tested are displayed in Figure 3, where the yellow rectangles mark the correctly detected targets and the red ones denote the false alarms. Missed ships have red circles.

With respect to the PWF detector, the conventional two-parameter CFAR was conducted to the composite image of PWF. To be specific, the guard and clutter windows, consisting of the hollow sliding window setup for the CFAR detector, were set as 45 × 45 pixels and 50 × 50 pixels, respectively. To ensure that the maximum numbers of large-size targets and low-intensity small targets were detected, the probability of false alarm was set to a high value of ${10}^{-3}$. Shown in Figure 5a, it can be seen that two small targets were missing, i.e., “T11” and “T20”. There were over 16 false alarms, most of which were generated by both azimuth ambiguities and the blurring regions surrounding targets such as “T1”, “T12” and “T18”.

For the tested PNF detector, the NPNF detector and for the proposed method, the same parameters of $\mathrm{RedR}$ and detection threshold T were adopted for the purpose of fair comparison. To be specific, according to Equation (6), a typical value of $T=0.98$ was selected, resulting in an approximate value of $\mathrm{RedR}=2\times {10}^{-3}$. The corresponding results of the three methods are given in Figure 5b,c,e, respectively. The proposed method ranked top in terms of target detection rate, followed by NPNF with two missing ships. The PNF detector ranked last with three missed targets. It was noted that all methods failed to detect target “T20”. With respect to the false alarm rate, the NPNF detector performed best with only three false targets, followed by our proposed method with four false alarms.

In [33], a new SPAN image of PolSAR data was constructed with the PCDM. Thus, the magnitude of target and azimuth ambiguities could be enhanced, while that of sea clutter suppressed. The PSH feature was designed for ambiguity discrimination, based on the eigenvalue–eigenvector decomposition of PCDM. There are two parameters in the PCDM method: the SPAN detection threshold $T_{span}$ and the threshold $T_{psh}$ for discriminating azimuth ambiguities from targets. In the experiment, according to the relative setting in [33] and the sensitivity test, the values of $T_{span}$ and $T_{psh}$ were set as 2.5 and 0.01, respectively. Therefore, the best performance of PCDM could be guaranteed. The detection result of the PCDM method is presented in Figure 5d. According to a comparison with the ground-truth, there were two missed ships (“T16” and “T20”) and three false alarms, two of which were caused by imaging blurring and one by ghost target “A12”. Some of the target pixels were missing, resulting in holes and unconnected components in the target region.

The quantitative accuracy assessment is provided in

Table 2. Detection Performance for C-Band AIRSAR Kojimawan Bay Image.

Comparative Methods	${\mathit{N}}_{\mathit{dt}}$	${\mathit{N}}_{\mathit{fa}}$	${\mathit{P}}_{\mathit{d}}$(%)	${\mathit{P}}_{\mathit{fa}}$(%)	$\mathbf{FoM}$(%)
PWF	19	>16	90.48	>45.71	<51.35
PNF	18	>14	85.71	>43.75	<51.42
NPNF	20	11	95.24	35.48	62.50
PCDM	19	3	90.48	13.64	79.17
Proposed	20	4	95.24	16.67	80.00

. Compared with other approaches, the proposed method gained the best performance with the highest value of $\mathrm{FoM}$, which was 80%, followed by the PCDM (79.17%), NPNF (62.50%), PNF (<51.42%), and PWF (51.35%), with values of $\mathrm{FoM}$ ranging from high to low. In terms of detection rate, the proposed method and NPNF both achieved the greatest value of $P_d$ with 95.24%, while the PWF and PCDM tied for second place with s 90.48% detection rate. With respect to the ability of false alarm removal, the PCDM ranked top with $P_{fa}$, this being 13.64%, followed by the proposed method with 16.67%. The PWF performed the worst with $P_{fa}$ being greater than 45.71%. By comparison, the proposed method performed better than the original PNF detector in [19] and the new form NPNF in [15], exhibiting properties of an improved detection rate and reduced false alarms.

5.2. Results and Analysis on the Second AIRSAR Dataset

The dataset for the second experiment was acquired from Tokyo Bay, Japan. After multilook processing, the corresponding resolutions in range and azimuth direction were 5.5 m and 13.5 m, respectively. The ground-truth of ship targets are marked with yellow rectangles in Figure 6. There were nine ship targets on the clam sea surface. Therefore, this was a relatively simple scene for target detection. However, it can be seen that there was azimuth ambiguity for ship “T1” and large-size cross-shape side lobes for target “T5”, which made it challenging to obtain detection results without false alarms.

The corresponding power images before the threshold processing are provided for Tokyo Bay in Figure 7 for the five methods tested. For fair comparison, the magnitude of each power image was normalized into the interval [0, 1]. According to the analysis above, the azimuth ambiguity “A1” and cross-shape side lobes of “T5” might cause false alarms in the detection results. With respect to the suppression of these two types of interferences, the PCDM and the proposed method performed better than other approaches. In Figure 7e,f, it can be seen, in the ${\lambda }_3$ image, that the intensities of both “A1” and the side lobes were reduced, yielding enhanced target results and suppressed interference in the power image of the proposed method. According to the direct visual effecta, though higher target-to-clutter contrast could be obtained by the PNF and NPNF, compared with the PWF, the intensities of ship targets, the azimuth ambiguity, and the side lobes were simultaneously magnified in the power images of PNF and NPNF.

The parameter settings for the CFAR detector for PWF and the comparative PNF detectors remained unchanged from those in the first experiment, the corresponding results of which are given in Figure 8. For the PCDM method, the values of $T_{span}=5$ and $T_{psh}=0.01$ were set. The corresponding result of the PCDM detector is shown in Figure 8d. By comparison, it can be observed that all tested methods successfully detected all ship targets. In terms of maintaining the shape integrity of targets, the PCDM was inferior to other methods, since many target pixels were dismissed as clutter, such as “T5”. With respect to the performance of ambiguity removal, other than our method, all the other tested approaches failed to remove the false alarm caused by the ghost target, “A1”. Both the NPNF detector and the proposed method successfully avoided false alarms resulting from the strong side lobes. In contrast, the performance of PWF suffered the most from the existence of side lobes, followed by the PNF detector.

The numerical analysis of performance for each detector in

Table 3. Detection Performance for C-Band AIRSAR Tokyo Bay Image.

Comparative Methods	${\mathit{N}}_{\mathit{dt}}$	${\mathit{N}}_{\mathit{fa}}$	${\mathit{P}}_{\mathit{d}}$ (%)	${\mathit{P}}_{\mathit{fa}}$ (%)	$\mathbf{FoM}$ (%)
PWF	9	>4	100	>30.77	<69.23
PNF	9	3	100	25.00	75.00
NPNF	9	2	100	18.18	81.82
PCDM	9	1	100	10.00	90.00
Proposed	9	0	100	0	100

validates the above conclusion drawn with basic visual effects. To be specific, all methods successfully detected all targets with $P_d$ being $100\%$. Due to the suppression of both azimuth ambiguity and side lobes, the proposed method obtained the best performance with the lowest $P_{fa}$ (i.e., 0) and greatest $\mathrm{FoM}$ (100%), followed by the PCDM ranking second with 10% $P_{fa}$ and 90% $\mathrm{FoM}$. The NPNF detector took the third place with 18.18% $P_{fa}$ and 81.82% $\mathrm{FoM}$, having slightly better performance than that of PNF (25% $P_{fa}$ and 75% $\mathrm{FoM}$).

5.3. Results and Analysis on the Third AIRSAR Dataset

The third dataset was obtained from Hiroshima Bay, Japan. To obtain better visual effects, the multilook processing was done in the azimuth direction with 9 looks. Thus, the resolutions in the range and azimuth directions were 5.5 m and 10.8 m, respectively. The subimage chosen for the test had a size of 600 × 600 pixels. Figure 9a presents the Pauli RGB image of the tested PolSAR dataset, marked with ground-truth information. It can be seen that there were three ship located on the sea surface, two of which had corresponding ghost targets caused by azimuth ambiguities. There was a cross-shaped side lobe, with quite a strong component in the azimuth direction.

The corresponding power images before the threshold processing for Hiroshima Bay are provided in Figure 10 for the five methods tested. For fair comparison, the magnitude of each power image was normalized into the interval [0, 1]. According to the analysis above, there were two azimuth ambiguities and cross-shape side lobes in the scene. As can be observed in Figure 10a–c, the PWF, PNF and NPNF failed to reduce the influence of azimuth ambiguities and side lobes. In contrast, both PCDM and the proposed method provided better interference suppression effects, according to the direct visual inspection.

With respect to the parameters of the PCDM detector, $T_{span}=5$ and $T_{psh}=0.01$ were set. The parameter settings for the CFAR detector and the comparative PNF detectors remained unchanged from those in the first two experiments. Since the imaging scene was the simplest of all tested datasets, all methods successfully detected all ship targets, as shown in Figure 11 and

Table 4. Detection Performance for Hiroshima Bay Image.

Comparative Methods	${\mathit{N}}_{\mathit{dt}}$	${\mathit{N}}_{\mathit{fa}}$	${\mathit{P}}_{\mathit{d}}$ (%)	${\mathit{P}}_{\mathit{fa}}$ (%)	$\mathbf{FoM}$ (%)
PWF	3	>4	100	>57.14	<42.85
PNF	3	>4	100	>57.14	<42.85
NPNF	3	>4	100	>57.14	<42.85
PCDM	3	1	100	25.00	75.00
Proposed	3	0	100	0	100

. With respect to the influence of azimuth ambiguities, the PWF, PNF and NPNF had similar detection results, where the two ghost targets were detected as true targets. Both the PCDM and the proposed method had no false alarms resulting from azimuth ambiguities. Furthermore, by comparison, it can be observed that the existence of side lobes interfere with all other methods, excluding the proposed method. Though the interference of side lobes posed less obstacles to the PCDM, less target pixels were detected. By contrast, our method obtained the best detection result, with all targets detected with integrity and no false alarms. This analysis can be further validated in Table 4.

To be specific, all methods successfully detected all targets with $P_d$ being $100\%$. Due to the suppression of both azimuth ambiguity and side lobes, the proposed method obtained the best performance with the lowest $P_{fa}$ (i.e., 0) and greatest $\mathrm{FoM}$ (100%), followed by the PCDM with 25% $P_{fa}$ and 75% $\mathrm{FoM}$. Due to the existence of side lobes and azimuth ambiguities, the PWF, PNF and NPNF obtained similar detection performances with $P_{fa}$ greater than 57.14% and $\mathrm{FoM}$ less than 42.85%.

6. Conclusions

In this paper, a modified polarimetric notch filter was proposed for ship detection in PolSAR imagery. The proposed method takes full advantage of the capability of the third eigenvalue ${\lambda }_3$ in suppressing azimuth ambiguities and side lobes. Combining this with the ${\lambda }_3$ value, the new feature vector was generated and utilized to construct a modified target power feature, based upon which the proposed PNF detector was obtained. Based on three C-band AIRSAR datasets, the new detector was tested against other excellent detectors, including the PWF detector, two PNF detectors and the PCDM- based azimuth ambiguity removal method. The comparative results demonstrated the capability of the proposed method in removing false alarms generated by both azimuth ambiguities and side lobes, and, thus, achieved improved detection performance.