# Infrared Dim and Small Target Detection Based on the Improved Tensor Nuclear Norm
## 6 Results and Analysis
### Sequence Image Detection Experiments
The SRWS algorithm constrains the sparse terms in the model using the overlapping edge information (OEI) in the background structure and then extracts the clutter by multiple subspaces. The SRWS algorithm constrains the sparse terms in the model using the background structure overlapping edge information (OEI) and then extracts the clutter through multiple subspaces, but the algorithm still cannot completely suppress it in the face of strong noise, as shown in (10), (11) and (13). As shown in (9)-(14), this paper suppresses the background in the a priori model based on the PSTNN algorithm and further enhances the target energy by combining the idea of high-order accumulation, which achieves better results compared with the remaining nine algorithms. To quantitatively compare the effect of this paper's algorithm with the remaining nine algorithms, the global signal-to-noise ratio and background suppression factor were used as evaluation indexes to evaluate the algorithm presented in this paper, and the results are shown in Tables 1 and 2. The maximum values are marked in bold in the table; we can see that the algorithm presented in this paper has a great advantage in terms of the global signal-to-noise ratio and background suppression of the difference map in six sequences compared to the other nine algorithms. In addition, the running speed of the algorithm is an important metric to evaluate the algorithm. The average single frame running time for all methods is shown in Table 4. From the table, we can see that compared with similar algorithms of VATF, SRWS, and PSTNN, the running speed of the proposed model in this paper is significantly reduced. Although the algorithm in this paper does not outperform the rest of the traditional spatiotemporal filtering algorithms in terms of running time, this drawback is acceptable in terms of overall performance. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **Scene 1** & **Scene 2** & **Scene 3** & **Scene 4** & **Scene 5** & **Scene 6** \\ \hline Anisotropy & 0.030574 & 0.02761 & 0.027462 & 0.027965 & 0.026676 & 0.055889 \\ Top\_hat & 0.076485 & 0.078233 & 0.07718 & 0.07832 & 0.078751 & 0.219467 \\ mpcm & 0.233488 & 0.237644 & 0.234299 & 0.260856 & 0.229161 & 1.204722 \\ GST & 0.013985 & 0.013881 & 0.013755 & 0.013982 & 0.015546 & 0.030258 \\ VATF & 1.266642 & 1.231002 & 1.223736 & 1.258206 & 1.365244 & 5.830361 \\ FKWR & 0.210284 & 0.178647 & 0.023463 & 0.225881 & 0.121728 & 0.572601 \\ SRWS & 2.709106 & 2.65044 & 2.66639 & 3.104156 & 2.903653 & 377.79159 \\ Aadcdd & 0.025507 & 0.036414 & 0.036629 & 0.033213 & 0.038618 & 0.151683 \\ PSTNN & 0.3873 & 0.404629 & 0.414345 & 0.407923 & 0.325582 & 1.659501 \\ Proposed & 0.253116 & 0.221659 & 0.224719 & 0.221864 & 0.204717 & 1.146247 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average single frame run time for all methods. (Unit: seconds). To further compare the performance of the algorithm presented in this paper with the other nine algorithms, we used ROC curves; the ROC curves are shown in Figure 15 below. As shown in Figure 15a-f, compared with the other nine algorithms, the algorithm presented in this paper still obtains a better target detection effect in terms of noise and edge contour suppression in the detection of sequence images based on the combination of the PSTNN model and the a priori model. As shown in Figure 15b-e, the anisotropic algorithm is unable to effectively separate the target and contours when performing background modeling in the face of the highlighted background contours, resulting in a lower detection rate. As shown in Figure 15f, the GST algorithm is unable to effectively detect the target point when the target point is submerged in the cloud layer, resulting in effective edge suppression when facing the junction edge of the cloud layer and the empty background at the same time. This leads to a high false alarm rate and a low detection rate in this scene.