## 3 Experimental Section
### Experiment Result of One Layer  
Experimental results using the PFT algorithm are shown in Figure 3. The same image in Figure 2 are used to be the example.  
Figure 3a is the saliency map after PFT calculation. Figure 3b is the result of threshold operation. Parameter k in threshold is set to be 0.3. It can be seen that the target has more saliency, which will help to improve detection rate and reduce false alarm rate. Figure 3c shows the detection result where all the targets are labeled in rectangles.  
Figure 2: One of the real infrared (IR) images for experiment.  
To demonstrate the detection effect of the proposed algorithm, we compare it with other three IR small target detection methods, including traditional top-hat algorithm (See Figure 4), two-dimensional least mean square (TDLMS) algorithm (See Figure 5) and HFT algorithm (See Figure 6). Here follows a brief introduction of top-hat algorithm and TDLMS algorithm.  
Top-hat is a mathematical morphology operation based on two basic operations: Dilation and erosion. The two basic operations includes the opening operations which smooth bright small regions of images  
Figure 4: Figures of top-hat. (**a**) saliency map of top-hat method; (**b**) result of threshold operation; (**c**) final result marked by blue block.  
Figure 5: Figures of two-dimensional least mean square (TDLMS). (**a**) saliency map of TDLMS method; (**b**) result of threshold operation; (**c**) final result marked by blue block.  
Figure 3: Figures of phase spectrum Fourier transform (PFT). (**a**) saliency map of PFT method; (**b**) result of threshold operation; (**c**) final result marked by blue block.  
and the closing operations which eliminate dark small holes Top-hat can be defined as the result of subtracting the original image from the opening operation of the original image and the structuring element. So, it can be used directly to detect potential targets.  
TDLMS filter acts as a background prediction operator when applied to the infrared small target detection. The filter can predict the image background with a long correlation length accurately. However, when the filter window moves to the area containing small targets which have a smaller correlation length, it will not be able to converge to the optimal solution. This method utilizes this property to separate small targets from the infrared image.  
In these three figures, (a) is the preprocessing result of the algorithm. (b) is the result after the same threshold operation as the proposed algorithm. (c) is the detection result. To reveal the advantages of the proposed algorithm to the other three algorithms, set algorithms threshold to different values and compare the detection rate [true positive rate (TPR) defined in (9)].  
\[TPR=\frac{Quantity\ \ of\ \ \ true\ targets\ detected\ in\ \ images}{Quantity\ \ of\ \ true\ targets\ existing\ in\ \ images}\times 100\% \tag{9}\]  
Experimental results (we will show them in Section 3.2) show that the parameter k in Equation (6) is suitable to be set from 0.36 to 0.5 in our work. We can get high TRP with all kinds of algorithms by selecting this parameters section so as to meet the requirements. At the same time, we can get the conclusion that PFT can achieve the best performance in TPR. TDLMS algorithm and top-hat method have lower TPRs. HFT method is obviously not suitable for small target, which makes its TPR lowest in all methods.