Ship Detection in Spaceborne SAR Images under Radio Interference Environment Based on CFAR

Abstract

Spaceborne synthetic aperture radar (SAR) can be easily interfered with by narrowband radio frequency interference (RFI) from ground radiation sources, causing significant degradation of image quality. In the application of SAR ship detection, the radio interference will raise the detection threshold of a constant false alarm rate (CFAR) detector, and consequently results in the degradation of detection performance. In order to solve this problem, we propose a ship-detection method for SAR under a narrowband RFI environment. The proposed method is mainly divided into five steps: (1) transform the input SAR image with narrowband RFI into 2-D frequency domain by fast Fourier transform (FFT); (2) use CFAR detector to detect RFI in 2-D frequency domain; (3) suppress RFI data points using adaptively weighting in the 2-D frequency domain; (4) transform the RFI suppressed 2-D spectrum into the image domain via inverse FFT; (5) apply CFAR detector for ship detection. Simulation and real data experiments show that the proposed method can effectively detect ships from SAR images with ocean background even if there exists serious RFI.

1. Introduction

Spaceborne synthetic aperture radar (SAR) is an imaging radar mounted on an artificial earth satellite, which relies on the use of electromagnetic waves within microwave frequency bands (typically, from P band to Ka band). Because it is not limited by the lighting conditions, spaceborne SAR can perform all-day and all-weather earth observation, providing an important remote sensing tool in both civil and military applications [1,2].

However, the microwave spectrum is shared by different radio applications. When other types of radio equipment use the same frequency band as a SAR satellite, these equipments will cause potential RFI to the SAR satellite. The C/X band with the center frequency of about 5.4 GHz and 9.6 GHz and the bandwidth of less than 300 MHz is often used for spaceborne SAR. Due to spectrum sharing, these SARs are faced with radio frequency interference (RFI). Up to now, such interference has been observed by many SAR sensors, such as sentinel-1A/B, Radarsat-2, RCM constellation, and Gaofen-3 [3,4,5,6]. L band interference was also reported in ALOS POLSAR observation [7]. These interferences will greatly deteriorate the image quality of spaceborne SARs, causing difficulties for many down-stream applications, one of which is SAR ship detection.

Ship detection is an important application of SAR. Researchers have proposed many methods for this task, e.g., deep learning based detectors [8,9,10,11], superpixel detectors [12,13,14,15], polarimetric SAR detectors [16,17,18,19,20,21] and constant false alarm rate (CFAR) detectors [22,23,24,25]. These methods are effective if the SAR image is clean, however, if the SAR images are corrupted by RFI, these methods will have performance degradation and even fail. In order to suppress RFI in SAR for subsequent information retrieval, a number of signal-processing methods have been proposed for RFI detection [26,27,28,29] and removal [28,30,31,32,33,34,35,36]. According to the RFI bandwidth, RFI removal methods can be divided into narrowband and wideband RFI suppressing methods. Narrowband RFI suppressing methods include notch filtering, eigen subspace filtering, etc. [34,37,38]. Wideband ones include frequency-domain notch filtering and improved eigen subspace filtering [39,40]. It is also notable that many optimization-based methods have been proposed in recent years [28,41,42,43,44,45,46]. Deep learning-based methods are also reported [47,48]. These RFI suppressing methods perform signal processing on SAR raw data to filter out RFI. For the focused SAR image, the above methods based on raw data processing are not applicable. Then, for such polluted SAR images, it will be difficult to apply for ship detection applications.

In this paper, we proposed a simple yet efficient processing flow for ship detection from SAR images acquired under narrowband RFI environment based on CFAR, where the CFAR module is used for both RFI removal and ship detection. The processing flow consists of five steps: (1) 2-D fast Fourier transform (FFT), (2) CFAR detection of RFI, (3) adaptive 2-D spectrum weighting, (4) 2-D inverse FFT (IFFT), (5) CFAR detection of ships. The steps 1–4 are used to suppress RFI to obtain a relatively clean SAR image, and the last step is to perform ship detection from the clean image. Simulation and real data experiments show that the proposed method can effectively improve SAR ship detection performance under narrowband RFI environments.

2. Signal Model

In the presence of RFI, the signal model of SAR received signal can be expressed as the summation of three terms, i.e.,

$$S(t_a,t_r)=S_{\mathrm{scat}}(t_a,t_r)+J(t_a,t_r)+N(t_a,t_r)$$

(1)

where the three terms at the right of this equation denotes backscattered target echo, RFI, and noise respectively, and $(t_a,t_r)$ is the fast time and slow time variables. For narrowband RFI, its signal model can be expressed as the sum of several sinusoids,

$$J(t_a,t_r)=\sum _k{a}_k\left(t_a\right)exp\left(j2\pi f_k{t}_r\right)$$

(2)

The 2-D spectrum of the echo backscattered by a point target can be expressed as

$$S_{\mathrm{scat},2\mathrm{df}}\left(f_a,f_r\right)=W_r\left(f_r\right)W_a\left(f_a-f_c\right)exp\left\{j{\theta }_{2\mathrm{df}}\right\}$$

(3)

where $S_{2\mathrm{df}}\left(f_a,f_r\right)$ is 2-D Fourier transform of $S_{\mathrm{scat}}(t_a,t_r)$. The transformation of SAR raw data into a SAR image can be regarded as matched filtering (MF) operation, which can be modelled by multiplication by a MF function $H(f_a,f_r)$ in the 2-D frequency domain, i.e.,

$$\begin{array}{cc}\hfill \tilde{S}(t_a^{\prime },t_r^{\prime })& =F{T}^{-1}\left\{FT\left\{S(t_a,t_r)\right\{·H(f_a,f_r)\right\}\hfill \\ \hfill & =Q\left\{S_{\mathrm{scat}}(t_a,t_r)\right\}+Q\left\{J(t_a,t_r)\right\}+Q\left\{N(t_a,t_r)\right\}\hfill \\ \hfill & ={\tilde{S}}_{\mathrm{scat}}(t_a^{\prime },t_r^{\prime })+\tilde{J}(t_a^{\prime },t_r^{\prime })+\tilde{N}(t_a^{\prime },t_r^{\prime })\hfill \end{array}$$

(4)

where $Q\left\{·\right\}=F{T}^{-1}\left\{FT\left\{·\right\{·H(f_a,f_r)\right\}$ is the matched filter. This fact shows that the bandwidth of $J(t_a,t_r)$ is preserved in $\tilde{J}(t_a^{\prime },t_r^{\prime })$, so we can still use narrowband signal model to describe $\tilde{J}(t_a^{\prime },t_r^{\prime })$, i.e.,

$$\tilde{J}(t_a^{\prime },t_r^{\prime })=\sum _k{a}_k^{\prime }\left(t_a^{\prime }\right)exp\left(j2\pi f_k{t}_r^{\prime }\right)$$

(5)

Therefore, we can use narrowband notch filtering to suppress RFI for subsequent ship detection in the SAR image. Although in SAR focusing algorithms the matched filter is spatially varying, the frequency band of RFI is still preserved in focused SAR images.

3. Ship Detection in SAR Images under RFI Environment

In the section, we introduce each step of our processing flow for ship detection from SAR images acquired under RFI environment.

3.1. Step 1: 2-D FFT

The first step is applying 2-D FFT to the SAR image,

$$\begin{array}{cc}\hfill {\tilde{S}}_{2\mathrm{df}}\left(f_a,f_r\right)=& {\tilde{S}}_{\mathrm{scat},2\mathrm{df}}\left(f_a,f_r\right)+{\tilde{N}}_{2\mathrm{df}}(f_a,f_r)+\int \tilde{J}(t_a,t_r)exp(-j2\pi f_a{t}_a-j{f}_r{t}_r)d{t}_a\hfill \\ \hfill =& S_{\mathrm{scat},2\mathrm{df}}\left(f_a,f_r\right)+{\tilde{N}}_{2\mathrm{df}}(f_a,f_r)\hfill \\ \hfill & +\sum _{k}T\mathrm{sinc}\left(\pi T(f_r-f_k)\right)\int a_k\left(t_a\right)exp(-j2\pi f_a{t}_a)d{t}_a\hfill \end{array}$$

(6)

where $\mathrm{sinc}\left(x\right)=\sin \left(\pi x\right)/\pi x$. The sinc function in the last line of this equation, $\mathrm{sinc}\left(T(f_r-f_k)\right)$, shows that the RFI in the 2-D frequency domain is a combination of several narrow responses. The total spectral occupation of the RFI, is thus the union of all the k bands,

$$B_{rfi}=\bigcup _k[f_k-1/T,f_k+1/T]$$

(7)

If the RFI energy is a few dB higher than the signal plus noise term, i.e., $S_{\mathrm{scat},2\mathrm{df}}\left(f_a,f_r\right)+{\tilde{N}}_{2\mathrm{df}}(f_a,f_r)$, the RFI will form a bright line in the 2-D spectral domain, and thus can be detected using CFAR as discussed in step 2.

3.2. Step 2: CFAR Detection of RFI

Considering the ocean environment, the backscattering coefficient is close to Gaussian clutter due to the speckle effect, and therefore the backscattering image spectrum, ${\tilde{S}}_{\mathrm{scat},2\mathrm{df}}\left(f_a,f_r\right)$, can be modelled as a Gaussian spectrum. In practice, SAR image spectrum of distributed scattering scenes usually can be viewed as a white Gaussian signal. Further considering that the noise spectrum is also white Gaussian, the detection of RFI in the 2-D spectral domain can be viewed as the problem of detecting a signal in the background of white Gaussian noise.

This can be achieved via CFAR detection, which perform adaptive binary thresholding using local clutter level estimate. This process can be described as follows,

$$M_1\left(f_a,f_r\right)=\left\{\begin{array}{cc}1,\hfill & \mathrm{if}|{\tilde{S}}_{2\mathrm{df}}\left(f_a,f_r\right){|}^2>{\alpha }_1{T}_1\left(f_a,f_r\right);\hfill \\ 0,\hfill & \mathrm{otherwise}.\hfill \end{array}\right.$$

(8)

where $M_1\left(f_a,f_r\right)$ indicates whether $\left(f_a,f_r\right)$ is decided to be a RFI frequency point, $\alpha$ is a scalar multiplier used to achieve desired probability of false alarm $P_{\mathrm{fa}}$, and ${\sigma }^2\left(f_a,f_r\right)$ is the estimate of local clutter spectral level. For the standard CFAR, $T_1\left(f_a,f_r\right)$ is obtained via averaging $N_1$ samples of $|{\tilde{S}}_{2\mathrm{df}}\left(f_a,f_r\right){|}^2$ selected around $\left(f_a,f_r\right)$ using a sample window

$$T_1\left(f_a,f_r\right)=\frac{1}{N_1}\sum _k{\left|{\tilde{S}}_{2\mathrm{df}}\left(f_a+x_k,f_r+y_k\right)\right|}^2,\left(x_k,y_k\right)\in H_1$$

(9)

where $H_1$ is a window consisting of pixel offset of local spectrum samples to the center sample. The multiplier is determined by $P_{\mathrm{fa}}$ and $N_1$, which is given by ${\alpha }_1=N_1(P_{\mathrm{fa},1}^{-1/N_1}-1)$.

3.3. Step 3: Adaptive RFI Weighting

Let us denote the set of frequency points detected to have RFI as ${\mathsf{\Omega }}_{rfi}$. For each frequency point in this set, i.e., $\left(f_a,f_r\right)\in {\mathsf{\Omega }}_{rfi}$, the signal model can be simply rewritten as

$${\tilde{S}}_{2\mathrm{df}}={\tilde{S}}_{\mathrm{scat},2\mathrm{df}}+{\tilde{N}}_{2\mathrm{df}}+{\tilde{J}}_{2\mathrm{df}}$$

(10)

For the reconstruction of ${\tilde{S}}_{\mathrm{scat},2\mathrm{df}}$, the linear estimation can be used via multiplying by a weighting variable $W_1\left(f_a,f_r\right)$, i.e.,

$${\widehat{\tilde{S}}}_{\mathrm{scat},2\mathrm{df}}=W_1{\tilde{S}}_{2\mathrm{df}}.$$

(11)

The estimation error is then given as

$$J=E|W_2{\tilde{S}}_{2\mathrm{df}}-{\tilde{S}}_{\mathrm{scat},2\mathrm{df}}{|}^2$$

(12)

where E denotes statistical expectation. Under the minimum square error criteria, the optimal $W_2$ is given as

$$W_1\left(f_a,f_r\right)=\underset{W_1}{\mathrm{argmin}}J=\frac{E|{\tilde{S}}_{\mathrm{scat},2\mathrm{df}}\left(f_a,f_r\right){|}^2}{E|{\tilde{S}}_{2\mathrm{df}}\left(f_a,f_r\right){|}^2}$$

(13)

for $\left(f_a,f_r\right)\in {\mathsf{\Omega }}_{rfi}$, and $W_1\left(f_a,f_r\right)$ = 1 for $\left(f_a,f_r\right)\notin {\mathsf{\Omega }}_{rfi}$. We can approximate $W_1$ using the following approximation,

$$\begin{array}{cc}\hfill & {\tilde{S}}_{\mathrm{scat},2\mathrm{df}}\left(f_a,f_r\right)={\sigma }^2\left(f_a,f_r\right)\hfill \end{array}$$

(14)

$$\begin{array}{cc}\hfill & E|{\tilde{S}}_{2\mathrm{df}}\left(f_a,f_r\right){|}^2\approx {\left|{\tilde{S}}_{2\mathrm{df}}\left(f_a,f_r\right)\right|}^2\hfill \end{array}$$

(15)

where the first equation is the local approximation used in CFAR, and the second equation is a one-shot approximation.

An alternative weight is the following 0–1 weight,

$$W_2\left(f_a,f_r\right)=\left\{\begin{array}{cc}0,\hfill & \mathrm{if}\mathrm{exist}(\nu ,\xi )\in {\mathcal{N}}_{\Delta }(f_a,f_r),\mathrm{s}.\mathrm{t}.M_1\left(\nu ,\xi \right)=1;\hfill \\ 1,\hfill & \mathrm{otherwise}.\hfill \end{array}\right.$$

(16)

where ${\mathcal{N}}_{\Delta }(f_a,f_r)=\left\{(\nu ,\xi )\right|\nu \in [f_a-\Delta ,f_a+\Delta ],\xi \in [f_r-\Delta ,f_r+\Delta ]\}$ is the neighbourhood of $(f_a,f_r)$. This masks out the any data point around detected the RFI frequency points with distance $\Delta$ in the 2-D frequency domain. It is notable that compared to other RFI suppressing methods, e.g., [49,50], the above weighting based method is simpler to implement.

In the following, we refer to (13) as weight 1 and (16) as weight 2, respectively.

3.4. Step 4: IFFT

With the RFI being suppressed or masked out in the 2-D spectrum, i.e., ${\tilde{S}}_{2\mathrm{df}}\left(f_a,f_r\right)·W\left(f_a,f_r\right)$, then an inverse FFT can be used to reconstruct the clean image

$$\widehat{\tilde{S}}\left(t_a^{\prime },t_r^{\prime }\right)={\mathcal{F}}^{-1}\left\{{\tilde{S}}_{2\mathrm{df}}\left(f_a,f_r\right)·W\left(f_a,f_r\right)\right\}$$

(17)

Doing so, we can reconstruct a clean SAR image in which the RFI is suppressed.

3.5. Step 5: CFAR Ship Detection

At last, CFAR can be used to detect ships in the clean SAR image, which can be expressed as follows

$$M_2\left(f_a,f_r\right)=\left\{\begin{array}{cc}1,\hfill & \mathrm{if}|\widehat{\tilde{S}}\left(t_a^{\prime },t_r^{\prime }\right){|}^2>{\alpha }_2{T}_2\left(t_a^{\prime },t_r^{\prime }\right);\hfill \\ 0,\hfill & \mathrm{otherwise}.\hfill \end{array}\right.$$

(18)

where $M_2$ is the binary pixel-wise ship detection result, ${\alpha }_2=N_2(P_{\mathrm{fa},2}^{-1/N_2}-1)$ is a scalar multiplier used to achieve a desired probability of false alarm $P_{\mathrm{fa},2}$, and $T_2$ is the clutter estimate defined as follows

$$T_2\left(t_a^{\prime },t_r^{\prime }\right)=\frac{1}{N_2}\sum _k{\left|\widehat{\tilde{S}}\left(t_a^{\prime }+x_k,t_r^{\prime }+y_k\right)\right|}^2,\left(x_k,y_k\right)\in H_2$$

(19)

where $H_2$ is a window consisting of pixel offset of clutter samples to the center sample.

Based on the above, we provide the full processing flow in Figure 1. From this diagram, we can see that the processing flow is very simple and thus has the benefit of easy implementation, which only main involves two function-modules, i.e., FFT/IFFT module and CFAR module.

4. Experiments

In this section, we use both simulated and real data to show the effectiveness of the proposed algorithm for SAR ship detection under a narrowband RFI environment. The performance of the algorithm is evaluated via the following metrics. The first metric is given as

$$Q_d=\frac{TP}{TP+TN},$$

(20)

where TP and TN denotes, respectively, the number of positive and negative detection of pixels in the labeled box of ships. This metric is the percentage of correctly detected pixels to the label box of ships, which can be viewed as the pixel-wise detection rate of the labeled pixels. The second metric is defined as follows

$$Q_{fa}=\frac{FP}{FP+FN},$$

(21)

where TP and TN denote, respectively, the number of positive and negative detections of pixels outside the labeled box of ships. This metric is the percentage of correctly detected pixels to the label box of ships, which can be viewed as the pixel-wise false alarm rate of the labeled pixels.

4.1. Experiment Using Simulated Data

In this experiment, we use a RFI-free Gaofen-3 SAR image with a ship as the clean images, and manually add simulated RFI artefacts to this image. The image is a $800\times 800$ patch extracted from a Gaofen-3 fine-stripmap 2 HH image acquired on 20 January 2018 around (E19.7, N58.3). The sampling bandwidth of SAR is 66.6 MHz, and the RFI bandwidth is 1 MHz. The simulated RFI-polluted image is shown in Figure 2a, where range direction is horizontal and azimuth direction is vertical.

To better show the processing steps in the proposed method, we provide several images of data flows of this experiment in Figure 2b–f. Figure 2b is the 2-D image spectrum, which is obtained after the first step of the proposed algorithm. The bright vertical strip is the simulated narrowband RFI. Figure 2c is the CFAR detection results of RFI data point in the 2-D frequency domain, which is obtained after the second step of the proposed algorithm. Bright pixels denote positive detection results. Figure 2d is the weighted 2-D spectrum using the proposed adaptive weight in step 3. After this step, we can see that most RFI data are effectively suppressed in the 2-D spectrum. Figure 2e is the output clean image obtained by applying IFFT to the weighted spectrum in step 4. In this image, we can see that most RFI artefacts are now significantly suppressed. Figure 2f is the is the CFAR detection results of ships from the clean image, where bright pixels are positive detection results, which correspond to the ship and outliers.

4.2. Experiments Using Real Data

In this experiment, we use Gaofen-3 SAR image acquired under a narrowband RFI environment. The image is a $2000\times 1000$ patch extracted from a Gaofen-3 fine-stripmap 2 HH image acquired on 13 February 2019 around (E129.3, N31.9). The sampling bandwidth of SAR is 66.6 MHz, and the RFI band consists of several discontinuous bands less than 1 MHz. This experiment image and associated data flow in the processing steps are visualized in Figure 3a–f.

4.3. Quantitative Analysis

In order to quantitatively evaluate the performance of the proposed algorithm, we calculate $Q_d$ − $Q_{fa}$ curves for four different experiment images, which are shown in Figure 4. The first and second images are those shown in Figure 2a and Figure 3a, respectively, and the third and fourth images are given in Figure 5a,b, respectively. The curve of $Q_d$−$Q_{fa}$ obtained without spectrum weighting are compared with that obtained using two weighting method discussed in the previous section.

In Figure 4a,d, we can see that the proposed algorithm, using either weight 1 or weight 2, can effectively improve the detection performance in terms of higher $Q_d$, i.e., the ratio of correctly detected pixels in the label box. For example, in Figure 4d, $Q_d$ obtained via using weight 1 and weight 2 are 0.5 and 0.14 higher than that obtained without using spectrum weighting.

In Figure 4b,c, $Q_d$ obtained via using weight 2 is always higher than that obtained without using spectrum weighting. However, this does not hold for that obtained using weight 1. This implies that weight 2 is more robust than weight 1.

5. Conclusions

In this paper, we proposed an efficient processing flow for ship detection in SAR images under a narrowband RFI environment. First, we formulate an SAR received signal model containing narrowband RFI, and we use matched filtering analysis to show that the RFI is also narrowband in the image domain. Then, we propose a CFAR based processing flow for ship detection in SAR images under a narrowband RFI environment, which works in a manner of RFI removal followed by ship detection. The overall processing flow consists of five steps: (1) 2-D FFT, (2) CFAR detection of RFI, (3) adaptive 2-D spectrum weighting for RFI suppression, (4) 2-D IFFT, (5) CFAR detection of ships.

We test the effectiveness of the proposed method using both simulated data (real SAR image plus simulated RFI) and real data (Chinese Gaofen-3 spaceborne SAR image acquired under RFI environment). Experimental results show that the proposed method can effectively improve detection performance.