# Spectra-Based Selective Searching for Hyperspectral Anomaly Detection
## 4 Discussion
### Quantitative Analysis  
In order to distinguish the ROC curves of these six algorithms for easier analysis, when drawing the ROC curve, we performed a logarithmic operation on the horizontal axis (FPR). Since the horizontal axis of the ROC curve was FPR and the vertical axis was TPR, it could be seen that when the ROC curve got a larger TPR under a smaller FPR, that is,when it approached the upper left corner of the coordinate space earlier, the algorithm had better anomaly detection performance. For the AVIRIS San Diego airport hyperspectral dataset, Figure 7 shows the ROC curves of different anomaly detectors for the quantitative comparison of detection performance. As we can see from Figure 7, the proposed Triple-S method was superior to the other detection methods for this dataset. When the false-alarm rate changed from 0.0001 to 1, the detection probability of the Triple-S method was always higher than those of other methods. The reason was that the proposed Triple-S algorithm had a purer background and the separation between the background and anomaly was maximal, which improved detection accuracy, compared with those algorithms for comparison. When the false alarm rate was low, the probability of detection was much higher than other methods, which corresponded to the relatively sharp rise of the detection probability curve of the Triple-S method. The ROC curve of the proposed Triple-S detection method was closest to the upper-left corner than those of the other algorithms. Moreover, the corresponding AUC values of these methods were calculated and reported in the first row of Table 1. Except for GRX, the other five algorithms had an AUC value close to 1. In the GRX, all of the pixels in the entire image were used as the background to calculate the background statistics, so the background statistics were seriously polluted by noise and abnormalities, resulting in poorer detection performance. The Triple-S algorithm we proposed had the highest AUC value. The AUC score of the Triple-S method was 0.9997, due to the full use of spatial and spectral information making the distinction between background and anomalies more accurate and complete. Figure 8 shows the ROC curve as a quantitative comparison of different anomaly detectors for the HYDICE Urban hyperspectral dataset. Due to the number of anomaly pixels in the Urban dataset being smaller than that of the San Diego airport dataset, the steps in the shape of the ROC curve were more obvious. All of the six ROC reached the maximum value faster. Among them, the ROC curve of the proposed Triple-S detection method was closest to the top-left corner, indicating superior detection performance. All of this proves the effectiveness and superiority of our proposed algorithm in the detection of hyperspectral anomalies. Moreover, the corresponding AUC values of these methods are calculated and reported in the second row of Table 1. The AUC score of the Triple-S method was 0.9998, which was larger than those of the other detectors. The reason was that the Triple-S algorithm not only effectively detected abnormal pixels, but also successfully suppressed background pixels. This can be attributed to the regions composed of adjacent pixels with the same spectral information, which effectively combined the advantages of hyperspectral information with image spatial information. The runtime performances of all the aforementioned methods were also recorded and compared, as presented in Table 2. The running time of the GRX was shortest due to the simple algorithm process. The calculation time of FEBPAD was shorter than that of FFE, and the reason was that the calculation order of FrFT was directly given in FEBPAD while there was a process of finding the best calculation order in FFE. The running time of LSAD-CR-IDW algorithm was the longest since the calculation process was the most complicated involving LSAD and CRD. The computing time of our proposed Triple-S algorithm depended on the size of the test image.