## 3 Results and Discussion
### Beach Analysis of the Plane Image Experiment Results  
(1) Parameter setting  
This experimental data include the sea surface, beach, island, aircraft, and other objects. One aircraft on the sea surface is the abnormal object and the rest is the background. For the algorithm of this paper, the main parameters involved are the parameters \(\sigma_{\text{sedw}}\), \(\sigma_{\text{svdw}}\), and \(\sigma_{\text{Lgd}}\) that control the corresponding output sensitivity in the improved trilateral filtering. There is also the threshold \(th\) for possible exception objects, which cooperatively represent regularization parameters \(\lambda\), and the corresponding size of the inner (\(W_{\text{in}}\)) and outer windows (\(W_{\text{out}}\)). It is verified by experiments that it has little effect on the final result, and it is uniformly set to \(10^{-6}\) for the regularization parameter \(\lambda\) 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 5, 5, and 1. The size of the inner and outer windows, \(W_{\text{in}}\) and \(W_{\text{out}}\), are 13 and 17, and the threshold \(th\) is set to 0.9. (2) Results and discussion  
The experimental simulation results of each algorithm on the Beach_Plane images are shown in Figure 5. Figure 5a shows the true value of the abnormal objects corresponding to the dataset, and Figure 5b-i shows the abnormal detection results of each comparison algorithm and the algorithm of this paper. In Figure 5, all algorithms can detect abnormal objects. However, the shape contour of abnormal objects in the detection results of the LRX algorithm is not as clear as other algorithms. In terms of background suppression, the algorithms of this paper, the LRX algorithm and CRD algorithm, have good background suppression effects, while the LRASR and KIFD algorithms have poor background suppression effects on this dataset, with a large number of obvious background residues. This indicates that there will be obvious false alarms for the LRASR and KIFD algorithms while not for the proposed algorithm. In order to observe the test results more clearly, the three-dimensional display of the test results is further analyzed subjectively on the basis of Figure 5. Figure 6 shows the corresponding 3D display of the test results. Figure 6a shows the three-dimensional distribution of real abnormal objects, and Figure 6b-i shows the three-dimensional grid corresponding to the detection results of all the algorithms. In the 3D grid of the experimental results in Figure 6, it can be seen clearly that the LRX algorithm has the best background suppression effect. However, the amplitude of some abnormal objects is small for this algorithm, and the degree of abnormal object retention is slightly worse than other algorithms. The serious background residue can be observed by the LRASR algorithm on this dataset. The object detection property of the KIFD algorithm is the best, but there are still many island background residues. In the detection results of the RX, CRD, WSCF, RPCA-RX, and the algorithms of this paper, the detection of abnormal objects is obvious. The amplitude in the background region of the CRD algorithm and the algorithm of this paper is relatively small, which indicates a good background suppression effect. The amplitude in the background region of other comparison algorithms is relatively large, and thus the background suppression effect of them is not as good as that of the CRD algorithm and the algorithm of this paper. Compared with the contrast algorithm, the algorithm of this paper has better subjective visual effects on object detection and background suppression in this experimental dataset. Further quantitative parameter analysis and evaluation was carried out on the detection results of the algorithms of this paper and comparison algorithms.