## 3 Ambiguity Suppression Method
### Ambiguous Area Detecting Based on CFAR  
The imaging result of main ambiguous area includes not only ambiguous targets but also range defocusing results of the main area and other ambiguous areas which show weaker backscattering intensity than focusing ones, bringing about even weaker intensity than the focusing ambiguous targets. The problem of ambiguous area target detection in the background of defocusing targets can be translated into the detection for strong backscattering targets under weak background, which is normally solved by a target detecting algorithm called CFAR [23; 24].  
Target detection based on CFAR is an algorithm that requires a given detection rate and a strong contrast between target and background, which is extensively used in ship detection of SAR image [25; 26]. The excellent results of ship detection demonstrate the ability of CFAR in strong scatter points detecting under weak background of SAR images, which is what we need for ambiguous area detection in this paper.  
In this paper we choose the double-parameter CFAR detection algorithm to achieve the detection of main ambiguous area targets [25; 26; 27; 28]. This algorithm sets up three sliding windows as shown in Figure 3 and realize the target detection by comparison of the pixel grayscale in target window and the self-adapting threshold which is acquired by false alarm rate (_PFA_) and background clutter modeling, which is assumed to be Gaussian distribution with mean value \(\mu\) and standard deviation \(\sigma\)in background window. The general flowchart is given in the left part of Figure 2. The specific steps are as follows.  
* Set up for the length of sliding windows  
The size of the general target window should be the same as the minimum size of targets to be detected. The length of the protection window is generally twice the maximum target size, while the background window being selected as two or four times the protection window size. The step length of the sliding window is in accordance with the size of the target window. The ambiguous area image is usually an integrated area composed of strong scattering points, different from ships which have a uniform shape, making it necessary to do some experiments to determine the reasonable length of the three windows.  
* Calculation of threshold including \(\mu\) and \(\sigma\) for the background window  
To set the detection threshold \(T\), we need the distribution function of background clutter and the given _PFA_. Supposing \(\Phi(\cdot)\) presents the Gaussian distribution function, we can get the following expression:  
\[T=\sigma\cdot t_{1}+\mu \tag{21}\] \[t_{1}=\Phi^{-1}(1-PFA)\]  
where \(\mu\) and \(\sigma\) are calculated according to each background window, making the threshold \(T\) changing adaptively. In fact, the background clutter may not be in conformity with the standard Gaussian distribution absolutely, forcing us to determine the reasonable choice of \(t_{1}\) through experiments.  
* Target detection  
If the gray value of a pixel in the target window is \(I_{tar}\), then the target detection criterion is:  
\[I_{tar}>\sigma\cdot t_{1}+\mu \tag{22}\]  
As mentioned above, we need some experiments to determine the reasonable parameters of the algorithm. Limited to the characteristics of the ambiguous area image itself, this method cannot evaluate the detection quality by the specific quantity of right detecting targets. We can only find a comparatively good value interval by comparing the results from visual observation.  
Figure 3: This is a figure that shows the geometric relation of three sliding windows. They are all squares and the inside is the target window, the middle is the protection window, and the outside is the background window.