## 3 Results and Discussion
### Experiment Results of the Saliens_Synthetic Image  
(1) Parameter setting  
In this experimental dataset, the scene includes vegetable garden, land, vineyard, and other ground object categories, including 12 synthetic anomaly objects. \(\lambda\) is set to be \(10^{-6}\) for the regularization parameter in the collaborative representation. The parameters in the improved trilateral filtering \(\sigma_{\text{sedw}}\), \(\sigma_{\text{svdw}}\), and \(\sigma_{\text{Lgd}}\) are set to be 3, 3, and 3. The size of the inner and outer windows, \(W_{\text{in}}\) and \(W_{\text{out}}\), are 13 and 15, and the threshold \(th\) is set to 0.3.  
(2) Results and discussion  
The experimental results on this experimental dataset are shown in Figure 8. Figure 8a shows the true value of the abnormal object, and Figure 8b-i shows the abnormal detection results corresponding to all algorithms. As can be seen from Figure 8, the LRX and CRD algorithms can only detect part of the objects in the experimental data, and the detected object contour size and other information are seriously lost. In the detection results of the RX, WSCF, and RPCA-RX algorithms, the object detection degree is poor, and some smaller objects are not obvious. The LRASR and KIFD algorithms can detect all objects, and the brightness of the detected objects is large, which indicates good detection properties. However, there are obvious background residues in the detection results of these two algorithms, indicating the false alarm detected by these algorithms. Compared to other contrast algorithms, the residual background was greatly reduced for the algorithm of this paper, and at the same time the relevant information such as the contour of the object is preserved while detecting all the objects.  
Figure 9a shows the 3D map of the real abnormal object, and Figure 9b-i shows the 3D grid map corresponding to the detection results of all algorithms. In Figure 9, the amplitude of each part can be clearly observed. In this experimental dataset, the LRX and CRD algorithms have a good background suppression effect, while there are missing cases of some objects. In the detection results of RX, WSCF, and RPCA-RX algorithms, the peak value at each object location is small, indicating that the object detection is not obvious. The LRASR and KIFD algorithms still have large numerical peaks outside of the object, and there are many background residues. The amplitude at each object location is large, and there is no large numerical peak residue outside of the object location for the algorithm of this paper, indicating good object detection and background suppression performance in comparison with other algorithms.  
The results of each algorithm are further analyzed and evaluated quantitatively. The corresponding ROC curves are shown in Figure 10, and the corresponding AUC values are shown in Table 2. In Figure 10, compared to other comparison algorithms, the ROC curve of the algorithm of this paper is closer to the upper left corner of the coordinate axis, indicating that the detection probability of the algorithm of this paper is better than that of the comparison algorithms under various false alarm rates. At the same time, the AUC values of RPCA-RX, KIFD, and the algorithm of this paper, are greater than the AUC values of other comparison algorithms in Table 2. The LRX, CRD, and LRASR algorithms show relatively poor detection performance.