## 4 Discussion  
We have compared the performance of our algorithms in public data sets, and our algorithm achieved high PSNR and SSIM in various types of images, achieving clearer image restoration results. With the enhancement of noise, our algorithm still maintains good performance compared with deep learning methods. Then, we remove noise under complex backgrounds with our method in IR image sequences, which effectively improves the PSNR and SSIM of IR image sequences. Additionally, in IR images, we achieve the best local SCRG of the small target. To achieve a better denoising effect, the parameters should be adjusted to match the real environment. In the meantime, as image complexity increases, our method maintains a high performance across all metrics.  
* Compared with traditional template filtering and sparse representation algorithms, our method outperforms them in regard to PSNR and SSIM in real IR images and public data sets under complex backgrounds.
* The deep learning methods could train an ideal model with a large amount of data sets with relatively low noise. It is slightly better than our method among all metrics. However, it does not obtain a good model with higher noise. Our method achieves better average PSNR and SSIM under high noise.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Noise Std** & \multicolumn{2}{c}{**20**} & \multicolumn{2}{c}{**50**} & \multicolumn{2}{c}{**75**} & \multicolumn{2}{c}{**100**} \\ \hline Metrics & PSNR & SSIM & PSNR & SSIM & PSNR & SSIM & PSNR & SSIM \\ \hline Mean & 31.399 & 0.818 & 27.029 & 0.540 & 24.039 & 0.366 & 21.824 & 0.255 \\ \hline Gaussian & 31.89 & 0.83 & 26.90 & 0.54 & 23.82 & 0.37 & 21.58 & 0.26 \\ \hline BM3D & 37.484 & 0.935 & 33.369 & 0.875 & 31.651 & 0.841 & 30.404 & 0.812 \\ \hline EPLL & 36.648 & 0.9 & 31.999 & 0.855 & 30.177 & 0.82 & 28.680 & 0.7 \\ \hline NSCR & 37.150 & 0.932 & 33.297 & 0.881 & 31.938 & 0.862 & 30.997 & 0.849 \\ \hline KSVD & 34.994 & 0.869 & 31.101 & 0.777 & 29.114 & 0.715 & 27.153 & 0.650 \\ \hline FFDNet & 38.2 & 0.941 & 34.2 & 0.888 & 32.11 & 0.861 & / & / \\ \hline ADNet & 37.32 & 0.932 & 33.65 & 0.875 & 16.52 & 0.062 & / & / \\ \hline GSR-WNNM & 37.027 & 0.925 & 33.249 & 0.866 & 31.861 & 0.842 & 30.859 & 0.816 \\ \hline Proposed & 37.15 & 0.928 & 33.388 & 0.872 & 32.156 & 0.864 & 31.416 & 0.858 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparison results of PSNR and SSIM with different denoising methods in Image(c).  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Method** & \multicolumn{2}{c}{**Image(a)**} & \multicolumn{4}{c}{**Image(b)**} & \multicolumn{4}{c}{**Image(c)**} \\ \hline
**Noise Std** & **20** & **50** & **75** & **100** & **20** & **50** & **75** & **100** & **20** & **50** & **75** & **100** \\ \hline Mean & 1.16 & 1.31 & 1.24 & 1.72 & 1.32 & 1.46 & 1.79 & 2.32 & 2.48 & 2.39 & 2.33 & 2.41 \\ \hline Gaussian & 1.08 & 1.38 & 1.45 & 1.65 & 1.37 & 1.39 & 1.63 & 1.91 & 2.22 & 5.08 & 2.81 & 2.84 \\ \hline BM3D & 2.4 & 2.33 & 2.42 & 2.63 & 2.49 & 2.80 & 2.89 & 2.95 & 1.17 & 4.24 & 4.37 & 4.36 \\ \hline EPLL & 1.52 & 1.74 & 1.73 & 1.91 & 2.19 & 2.34 & 2.39 & 2.47 & 1.11 & 1.04 & 3.52 & 5.43 \\ \hline NSCR & 2.44 & 2.61 & 2.63 & 2.73 & 2.49 & 2.41 & 2.52 & 2.78 & 1.18 & 3.66 & 6.91 & 7.19 \\ \hline KSVD & 1.59 & 1.71 & 2.33 & 2.43 & 1.41 & 2.05 & 2.66 & 2.84 & 1.29 & 1.84 & 4.01 & 5.46 \\ \hline FFDNet & 2.33 & 2.66 & 2.78 & / & 2.41 & 2.51 & 2.70 & / & 1.11 & 2.83 & 2.64 & / \\ \hline ADNet & 2.42 & 2.64 & 2.88 & / & 2.49 & 2.71 & 2.76 & / & 1.11 & 1.87 & 2.89 & / \\ \hline GSR-WNNM & 2.63 & 2.74 & 2.86 & 2.88 & 1.65 & 2.49 & 2.585 & 2.59 & 1.05 & 1.16 & 6.81 & 6.99 \\ \hline Ours & 2.44 & 2.81 & 2.87 & 2.89 & 2.57 & 2.71 & 2.76 & 3.69 & 1.22 & 4.15 & 6.93 & 7.41 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparison results of mean local SCRG of the small target with different denoising methods.  
These results have verified that the method with the adaptive GSR model could achieve stable and balanced effects under complex environments.