## 4 Experiment and Analysis of Experimental Results
### Subjective Evaluation in Different Scenes  
In this sub-section, we give the detection results of six infrared image sequences. The method proposed herein is compared with six related advanced methods, namely Top-Hat [41], IPI [9], PSTNN [22], IPT [23], WSNMSTIPT [24], and NRAM [16]. For the convenience of observing the results, the experimental results obtained and the three-dimensional grid diagrams generated by all the test methods in different scenarios are given intuitively in Figures 5-10.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Methods** & **Parameter Setting** \\ \hline Top-Hat & Structure size: \(3\times 3\), structure shape: square \\ PSTNN & Sliding step : \(40\), \(\lambda=0.6/\sqrt{max(n_{1},n_{2})*n_{3}}\), patch size: \(40\times 40\), \(\epsilon=1\times 10^{-7}\) \\ IPI & Patch size : \(50\times 50\), sliding step : \(10\), \(\lambda=1/\sqrt{min(m,n)}\), \(\epsilon=10^{-7}\) \\ RIPT & Patch size : \(30\times 30\), \(\lambda=L/\sqrt{min(m,n)}\), sliding step: \(10\), \(L=0.7\), \(h=1\), \(\epsilon=10^{-7}\) \\ WSNMSTIPT & Patch size : \(30\times 30\), sliding step : \(30\times L=6\), \(\mathrm{p}=0.8\), \(\lambda=1/\sqrt{max(n_{1},n_{2})*n_{3}}\) \\ NRAM & Patch size : \(50\times 50\), sliding step : \(10\), \(\lambda=1/\sqrt{min(m,n)}\), \(\mu 0=3\sqrt{min(m,n)}\), \\  & \(\gamma\ =0.002\), \(C=\sqrt{min(m,n)/2.5}\), \(\epsilon=10^{-7}\) \\ MNSTLA & Patch size : \(50\times 50\), sliding step : \(10\), \(\gamma=0.002\), \(\mu=c\sqrt{min(m,n)}\) where \(c=3\), \(L=3\), \(C=25\), \(\epsilon=1\times 10^{-7}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The parameters for the 7 tested methods.  
Figure 5: Infrared Sequence (a) Original image and Detection Results and the 3d grid diagrams.  
Figure 6: Infrared Sequence (b) Original image and Detection Results and the 3d grid diagrams.  
Figure 7: Infrared Sequence (c) Original image and Detection Results and the 3d grid diagrams.  
Figure 8: Infrared Sequence (d) Original image and Detection Results and the 3d grid diagrams.  
Figure 9: Infrared Sequence (e) Original image and Detection Results and the 3d grid diagrams.  
It can be seen from Figures 5-10 that the RIPT model has the worst detection efficiency; the Top-Hat and PSTNN methods do enhance the targets, but edges and noise are introduced, which is mainly due to the assumption of fixed structural elements and a smooth background. Undoubtedly, among all the results from the test methods, the Top-Hat and PSTNN methods have the worst performance. This is because this contrast mechanism is not suitable for complex backgrounds. The IPI method is slightly better than the Top-Hat and PSTNN methods. The WSNMSTIPT models are on account of the IPI model and refer to the spatial-temporal information. Compared with the IPI model, although their false alarm rates are effectively reduced, not only do the images with dim targets selected from data sets 13 and 17 (corresponding to Figures 7 and 9) lose their targets, but also the images selected from the data sets with complex backgrounds lose their targets. Compared with the WSNMSTIPT models, the NRAM model does not consider the spatial-temporal information; it constructs the target-patches and background-patches according to the sparse feature of infrared target images. It can be seen from Figures 5-10 that, compared with the IPI model, the NRAM method not only effectively reduces the false alarm rate but also effectively enhances the strong edges. Therefore, the potential target points are also enhanced, and a better detection rate is achieved compared with the IPI model. The MNSTLA model proposed herein constructs, on account of the NRAM model and the spatial-temporal information, a spatial-temporal tensor model of infrared dim moving targets that fully considers the correlation between the frames of infrared dim moving  
Figure 10: Infrared Sequence (f) Original image and Detection Results and the 3d grid diagrams.  
targets and can further reduce the false alarm rate and improve the detection efficiency of infrared dim moving targets.