## 3 Results  
The simulation uses MATLAB R2016a software and runs on a personal computer with Intel core i7 CPU and 16 GB RAM. We test our method in data sets (_set_12) and IR sequences using an IR detector. The typical gray images are widely used for simulation analysis. In Figures 1-12, the pixel size is 256 \(\times\) 256. Adding Gaussian noise with different std, we adopt a pair of different parameters. The results of the denoising effect are not the same in many experiments. We adjust the parameters to attain better denoising results. Setting the std of WGS as \(20,50,75,100\), separately, we choose the corresponding patch size 6 \(\times\) 6, 7 \(\times\) 7, 8 \(\times\) 8, 9 \(\times\) 9. Similar patches are designed with \(60,70,80,100\). Additionally, the reference index \(\tau\) and \(c\) are set to be \((0.0013,0.65)\), \((0.0012,0.55)\), \((0.001,0.75)\), \((0.0017,0.55)\). The searching windows could be 30 and the error \(\epsilon=\exp^{-15}\). The adaptive similar block setting parameter \(f\) is \(2*\exp^{-4}\). Finally, we complete all simulations based on our settings. The typical images including \((1)\),\((2)\), and \((3)\) are simulated and compared with the conventional spatial filtering and sparse representation denoising methods. When the noise std is \(20,50,75,100\), image PSNR and SSIM results are compared with Gaussian filtering, mean filtering, BM3D [10], EPLL [40], NSCR [41], KSVD [14], FFDNet [22], ADNet [23], GSR-WNNM [42], and our proposed method. Table 2 shows the denoising PSNR and SSIM of image \((1)\) with different noise std. Table 3 shows the denoising PSNR and SSIM of image \((2)\) with different noise std. Table 4 shows the denoising PSNR and SSIM of image \((3)\) with different noise std. Under the same noise std, the proposed algorithm outperforms traditional algorithms in terms of PSNR and SSIM. With the increase in the std of noise, the performances of traditional Gaussian filtering, mean filtering, BM3D, and other algorithms have significantly decreased, but the algorithm proposed in this paper can still have better PSNR and SSIM. Compared with classic deep learning algorithms, our method performs equally well with FFDNet and ADNet under low-noise environments. As the noise increases, the model training performance of deep learning decreases which results in a degradation in performance. Our method, on the other hand, still performs well. Under the condition of different noise std, using the Gaussian filter, mean filter, BM3D, EPLL, NSCR, KSVD, FFDNet, ADNet, GSR-WNNM, and the algorithm in this paper, the image \((1)\), \((2)\), \((3)\) denoising effects are shown in the supplementary materials. \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 & 25.4 & 0.74 & 23.83 & 0.55 & 22.15 & 0.42 & 20.54 & 0.33 \\ \hline Gaussian & 26.22 & 0.76 & 24.19 & 0.56 & 22.33 & 0.43 & 20.57 & 0.34 \\ \hline BM3D & 33.77 & 0.87 & 29.69 & 0.81 & 27.51 & 0.76 & 25.87 & 0.72 \\ \hline EPLL & 33.01 & 0.85 & 28.80 & 0.8 & 26.99 & 0.75 & 24.95 & 0.7 \\ \hline NSCR & 33.86 & 0.87 & 29.56 & 0.82 & 27.27 & 0.77 & 25.31 & 0.74 \\ \hline KSVD & 33.19 & 0.86 & 27.97 & 0.77 & 25.09 & 0.67 & 23.69 & 0.61 \\ \hline FFDNet & 34.03 & 0.87 & 30.31 & 0.83 & 28.31 & 0.79 & / & / \\ \hline ADNet & 33.92 & 0.87 & 30.38 & 0.826 & 16.96 & 0.18 & / & / \\ \hline GSR-WNNM & 34.07 & 0.87 & 30.25 & 0.82 & 28.26 & 0.79 & 26.86 & 0.76 \\ \hline Proposed & 34.1 & 0.88 & 30.39 & 0.83 & 28.4 & 0.8 & 26.88 & 0.78 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison results of PSNR and SSIM with different denoising methods in image \((1)\). With the increase in the Gaussian noise std, the proposed algorithm could attain a better denoising effect and clearer texture details compared with other methods.