# Infrared Dim and Small Target Detection Based on the Improved Tensor Nuclear Norm
## 6 Results and Analysis
### Sequence Image Detection Experiments  
In order to better demonstrate the performance of the algorithm in this paper, six sequences of infrared images were used. The backgrounds of the six sequences were complex, including grass, forest, bright road, clouds, buildings, etc. The target size was small, and there were no color information or fixed texture features [27]. These characteristics meet the application requirements for actual scenes, so the detection effect observed for these six sequences of scenes is of great practical significance. Representative images of the six scenes are shown in Figure 8; the specific descriptions are shown in Table 3.  
Figure 7: Detection results of the algorithm in this paper under 16 scenes. (**a–p**) are the detection results in 16 scenes, and the following is the three-dimensional map of the detection results. In order to highlight the detection effect, we took out a frame in six sequences and compared the detection results for the algorithm presented in this paper with those of nine algorithms in terms of the absolute average difference weighted by cumulative directional derivatives (Aadcdd) [28], the generalized structure tensor(GST) [29], via the non-convex tensor fibered rank (VNTR) [30], the facet kernel and random walker (FKRW) [31], the multiscale patch-based contrast measure (MPCM) [32], Anisotropy [33], the top-hat, the self  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sequence** & **Size/Pixels** & **Length/Frames** & **Description of Sequence** \\ \hline Seq. 1 & \(256\times 256\) & 100 & The target is in the shape of a dot, and the background of the picture is grass. \\ \hline Seq. 2 & \(256\times 256\) & 59 & The target is in the shape of a dot, and the background of the picture is a tree and a bright road. \\ \hline Seq. 3 & \(2  
Figure 11: Detection results of sequence 3. Figure 10: Detection results of sequence 2. Figure 12: Detection results of sequence 4. Figure 13: _Cont._  
From the detection results, it can be seen that the Aadcdd algorithm obtains the weighting coefficients for the average absolute gray difference by accumulating the directional derivatives, which makes up for the high false alarm rate defect caused by the average absolute gray difference in the face of a high-intensity structural background; however, as shown in Figure 10, the algorithm still produces an unsatisfactory suppression effect for the background when there is a large area of highlighted contours in the background. The GST  
Figure 14: Detection results of sequence 6. Figure 13: Detection results of sequence 5.  
algorithm models the dim and small target by the second conjugate of the two-dimensional Gaussian. The GST algorithm models the dim and small target by the second symmetric derivative of the two-dimensional Gaussian, but the suppression effect is not satisfactory in the face of strong noise, as shown in Figures 10, 11 and 13. The VNTR algorithm approximates the tensor fiber rank by tensor fiber kernel parametrization of the log operator based on the IPT model and suppresses the noise jointly with the hyperlocal variation and the PSTNN algorithm. The PSTNN algorithm is used as a non-convex approximation of the tensor rank by PSTN, but it can be seen from Figures 9-14 that the background is not further suppressed by the two algorithms in the local prior, resulting in a small number of contours in the final target image when facing a strong edge contour background. The FKRW algorithm achieves clutter suppression and target enhancement by the local contrast descriptor (NLCD). The FKRW algorithm achieves clutter suppression and target enhancement by the local contrast descriptor (NLCD), but the effect of strong edge contour suppression by this descriptor is not satisfactory, as shown in Figures 10-12. The top-hat, MPCM, and anisotropy algorithms are sensitive to noise and edges, resulting in a high false alarm rate in the final result.