## 3 Results
### Simulation Results for Filtering Additive Gaussian Noise and Speckle Noise
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & Train station & Music hall & Big Ben & Cambridge bldg & Gaudi bldg \\ \hline Noisy image PSNR & 29.1548 & 28.6296 & 27.3704 & 31.8288 & 27.7893 \\ BM3D 0.5\(\sigma\) & **34.2037** & **31.7623** & 31.0264 & **33.9564** & 31.1511 \\ BM3D 1\(\sigma\) & 32.576 & 29.4154 & 28.4644 & 30.9181 & 28.8088 \\ BM3D 1.5\(\sigma\) & 31.3591 & 27.5322 & 26.5578 & 29.005 & 26.6459 \\ Frost & 29.3017 & 25.5846 & 24.9998 & 24.3581 & 25.8356 \\ Lee & 30.7351 & 27.8267 & 26.4379 & 27.3616 & 27.5166 \\ MLMVN-S-1 & 33.4248 & 31.2865 & **31.8917** & 33.6882 & **31.4565** \\ MLMVN-S-2 & 32.9115 & 30.9381 & 31.7142 & 33.3546 & 31.1229 \\ MLMVN-S-3 & 33.1212 & 31.0855 & 31.798 & 33.5095 & 31.2845 \\ \hline  & Barcelona plaza & Sailboat & Manhattan & Airplane & Fighter-jet \\ \hline Noisy image PSNR & 27.7252 & 31.0785 & 30.229 & 32.2943 & 28.3538 \\ BM3D 0.5\(\sigma\) & 30.4968 & **37.1901** & 35.2554 & **38.5173** & 32.8427 \\ BM3D 1\(\sigma\) & 28.1887 & 33.9383 & 32.9065 & 37.7703 & **35.4343** \\ BM3D 1.5\(\sigma\) & 26.5971 & 32.4034 & 30.9719 & 35.5195 & 33.7933 \\ [PERSON] & 25.2128 & 30.1896 & 27.6313 & 29.9569 & 30.7026 \\ Lee & 26.8865 & 32.4212 & 29.8526 & 33.7633 & 33.3033 \\ MLMVN-S-1 & 31.8259 & 36.6313 & 35.3114 & 37.4804 & 35.4004 \\ MLMVN-S-2 & 31.5377 & 35.9756 & 34.7158 & 36.3381 & 35.0165 \\ MLMVN-S-3 & 31.677 & 36.3271 & 35.0075 & 36.851 & 35.1973 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of filtering grayscale images affected by multiplicative speckle noise with a standard deviation of 0.3\(\sigma\), where \(\sigma\) is the standard deviation of the ideal image. The best results are shown in bold, and the best results using our approach are highlighted in color. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & Train station & Music hall & Big Ben & Cambridge bldg & Gaudi bldg \\ \hline Noisy image PSNR & 26.7005 & 26.1868 & 25.1993 & 29.3454 & 25.3672 \\ BM3D 0.5\(\sigma\) & **32.4979** & **29.8616** & 29.2817 & 31.9489 & 29.4405 \\ BM3D 1\(\sigma\) & 31.1296 & 27.7225 & 26.7524 & 29.4297 & 27.1516 \\ BM3D 1.5\(\sigma\) & 30.0805 & 26.1482 & 25.2561 & 27.8733 & 25.5813 \\ Frost & 28.6894 & 25.267 & 24.6709 & 24.3052 & 25.6198 \\ Lee & 29.8741 & 27.2948 & 25.962 & 27.2305 & 27.2076 \\ MLMVN-S-1 & 30.886 & 29.402 & 29.3543 & 32.1551 & **29.4495** \\ MLMVN-S-2 & 30.5167 & 29.1159 & **29.3764** & 31.7958 & 29.2278 \\ MLMVN-S-3 & 30.6627 & 29.2276 & 29.3627 & 31.9539 & 29.3293 \\ \hline  & Barcelona plaza & Sailboat & Manhattan & Airplane & Fighter-jet \\ \hline Noisy image PSNR & 25.2747 & 28.584 & 27.7327 & 29.8389 & 25.858 \\ BM3D 0.5\(\sigma\) & 28.6345 & **35.0658** & **33.3732** & **36.879** & 30.7953 \\ BM3D 1\(\sigma\) & 26.9191 & 32.719 & 31.3977 & 35.9913 & **33.9965** \\ BM3D 1.5\(\sigma\) & 25.6379 & 31.5217 & 29.8046 & 33.8131 & 32.5234 \\ Frost & 25.0076 & 29.9046 & 27.4366 & 29.7582 & 30.1304 \\ Lee & 26.5529 & 31.9175 & 29.4938 & 33.1938 & 32.1024 \\ MLMVN-S-1 & 29.5072 & 34.3743 & 32.963 & 35.2263 & 33.2604 \\ MLMVN-S-2 & 29.3592 & 33.6725 & 32.421 & 34.1796 & 32.8563 \\ MLMVN-S-3 & 29.4303 & 34.0011 & 32.6647 & 34.6213 & 33.0585 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of filtering grayscale images affected by multiplicative speckle noise with a standard deviation of 0.4\(\sigma\), where \(\sigma\) is the standard deviation of the ideal image. The best results are shown in bold, and the best results using our approach are highlighted in color. Figures 8 and 9 present the results of filtering additive Gaussian noise and speckle noise, respectively, using the MLMVN and the BM3D filter. Images (a-d) illustrate the cases where the MLMVN achieved a higher PSNR than the BM3D filter. Images (e-h) show the cases where the PSNR values for both methods are approximately equal. Finally, images (i-l) depict the cases where the BM3D filter outperformed the MLMVN in terms of PSNR. Figure 8: (**a**) Ideal image. (**b**) Noisy image. Gaussian noise 0.2\(\sigma\). PSNR 28.9904 dB. (**c**) Image filtered using MLMVN.