# Modulus Stretch-Based Circular SAR Imaging with Contour Thinning
## 3 Experimental Results
### Vehicle Imaging in Gotcha Dataset  
The Target Discrimination Research subset of the Gotcha dataset published by the Air Force Research Laboratory for circular flight observations in a parking lot was used for the imaging test. The airborne synthetic aperture radar detects data in a 5 km diameter area on 31 altitude orbits and extracts phase history data of 56 targets from the large dataset. Targets include 33 civilian vehicles (with repeat models) and 22 reflectors and an open area. The circular synthetic aperture radar provides 360 degrees of azimuth around each target. A Chevrolet Impala LT model in the dataset was selected for the modulus stretch imaging with the data label fcarA1 and the orbit number 214. The results are shown in the following figure. Figure 8a shows the imaging of the traditional backprojection algorithm with a synthetic aperture of 5\({}^{\circ}\). Figure 8e is a full aperture imaging of the traditional backprojection algorithm. Figure 8b-d is the imaging results after piecewise linear transformation based on a 5\({}^{\circ}\) synthetic aperture. Figure 8f-h is the imaging results of a full aperture after piecewise linear transformation at each slow time \(\tau_{n}\). The parameter \(k_{1}\) of the piecewise linear transformation was a fixed value of 1.2, \(k_{2}\) was a fixed value of 0.1, and \(T\) was 0.5, 0.8 and 0.9, in order. It can be clearly seen from the figure that the vehicle image obtained by the traditional backprojection algorithm is fuzzy and cannot represent the contour structure and details of the vehicle well. The imaging results after piecewise linear transformation significantly improve the contour information of vehicle imaging and can distinguish the double-line fine contour on one side of the vehicle, which cannot be distinguished from the two close contours in the traditional backprojection algorithm imaging. These fine structures may play an active role in target recognition. At the same time, it is noticed that full aperture imaging can not only thin the contour, but also lose part of the contour details, which makes the imaging accuracy worse. However, the piecewise linear transformation based  
Figure 8: Imaging of vehicle targets in the Gotcha dataset by piecewise linear transformation with different thresholds: (**a,e**) No piecewise linear transform; (**b,f**) \(T=0.5\); (**c,g**) \(T=0.8\); (**d,h**) \(T=0.9\). on a synthetic aperture can thin the contour and lose less of the original contour, so the imaging result is better. Figure 9 is the image of four different models of vehicles after modulus stretched by piecewise linear transformation. Figure 9a-d is the imaging results of using the traditional backprojection algorithm for four models of vehicles, namely Chevrolet Impala LT, Mitsubishi Galant ES, Toyota Highlander and Chevrolet HHR LT. Figure 9e-f corresponds to Figure 9a-d for imaging after the modulus is stretched using piecewise linear transformation. The parameters of the piecewise linear transformation were \(k_{1}=1.2\), \(k_{2}=0.1\) and \(T=0.9\). It can be seen that the image of all models of vehicles after modulus stretched greatly strengthens the contour features of the target and improves the recognizability. Subsequently, target recognition can be carried out by detecting the aspect ratio of target contour, the relative position of internal and external contour, contour angle, and other features. In order to obtain the optimal threshold parameters of the piecewise linear transformation, different thresholds \(T\) were used for imaging different vehicles, and the degree of contour thinning was calculated. The curves are shown in Figure 10. As can be seen from the figure, when the threshold \(T\) is between 0.9 and 0.96, the degree of contour thinning reaches a maximum value and then decreases rapidly as \(T\) increases. The experiment shows that when \(k_{1}=1.2\) and \(k_{2}=0.1\), for most of the vehicle data in the Gotcha dataset, the maximum degree of contour thinning can be obtained when the threshold \(T\) is about 0.94.