## 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 & 32.6753 & 32.1159 & 30.3498 & 35.3354 & 31.2367 \\ BM3D 0.5\(\sigma\) & **36.7301** & **34.6453** & 33.3135 & **37.0061** & **33.7141** \\ BM3D 1\(\sigma\) & 34.6252 & 32.043 & 31.3216 & 33.6298 & 31.8137 \\ BM3D 1.5\(\sigma\) & 33.1557 & 29.8412 & 28.7203 & 31.0331 & 28.8251 \\ Frost & 29.8109 & 25.8298 & 25.2361 & 24.3977 & 26.0143 \\ Lee & 31.4611 & 28.2385 & 26.7904 & 27.4653 & 27.7698 \\ MLMVN-S-1 & 36.2585 & 33.1139 & 34.7767 & 35.0894 & 33.4302 \\ MLMVN-S-2 & 35.7398 & 32.8295 & 34.4242 & 34.8853 & 33.0994 \\ MLMVN-S-3 & 35.9468 & 32.9511 & 34.6287 & 34.9894 & 33.2681 \\ \hline \hline  & Barcelona plaza & Sailboat & Manhattan & Airplane & Fighter-jet \\ \hline Noisy image PSNR & 31.2046 & 34.6086 & 33.7206 & 35.7485 & 31.8837 \\ BM3D 0.5\(\sigma\) & 33.3862 & **40.3269** & **37.9508** & **40.786** & 35.6958 \\ BM3D 1\(\sigma\) & 30.4868 & 36.2671 & 35.3317 & 40.2067 & **37.5485** \\ BM3D 1.5\(\sigma\) & 28.2379 & 34.0124 & 32.9935 & 38.1526 & 35.7779 \\ Frost & 25.3471 & 30.4103 & 27.7662 & 30.1288 & 31.1936 \\ Lee & 27.0814 & 32.7945 & 30.0945 & 34.2327 & 34.3365 \\ MLMVN-S-1 & 34.0183 & 38.7255 & 37.6577 & 39.5762 & 37.1491 \\ MLMVN-S-2 & 33.7173 & 38.4703 & 37.2599 & 38.6982 & 37.1038 \\ MLMVN-S-3 & 33.8792 & 38.7025 & 37.4987 & 39.1209 & 37.1174 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of filtering grayscale images affected by multiplicative speckle noise with a standard deviation of 0.2\(\sigma\), 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 & 22.1619 & 22.9098 & 20.8601 & 24.6972 & 22.5851 \\ BM3D 0.5\(\sigma\) & 25.1578 & 25.0337 & 23.8199 & 26.3476 & 24.7072 \\ BM3D 1\(\sigma\) & **31.5803** & **28.8525** & **27.6952** & **30.2132** & **28.2913** \\ BM3D 1.5\(\sigma\) & 30.599 & 27.2943 & 26.0956 & 28.6788 & 26.4801 \\ MLMVN-G-1 & 27.8965 & 27.4263 & 25.4873 & 28.734 & 26.979 \\ MLMVN-G-2 & 27.9158 & 27.4332 & 25.5081 & 28.7452 & 27.0003 \\ MLMVN-G-3 & 27.865 & 27.4018 & 25.4714 & 28.7631 & 26.9621 \\ \hline  & Barcelona plaza & Sailboat & Manhattan & Airplane & Fighter-jet \\ \hline Noisy image PSNR & 22.1456 & 25.493 & 23.9169 & 25.5879 & 25.6751 \\ BM3D 0.5\(\sigma\) & 24.1643 & 28.0635 & 26.4294 & 28.3924 & 28.1542 \\ BM3D 1\(\sigma\) & **27.7561** & **33.763** & **32.1677** & **35.978** & **34.4722** \\ BM3D 1.5\(\sigma\) & 26.2848 & 32.1272 & 30.6002 & 34.8368 & 33.4473 \\ MLMVN-G-1 & 26.6104 & 31.725 & 29.6582 & 32.2901 & 32.6759 \\ MLMVN-G-2 & 26.6285 & 31.7205 & 29.6736 & 32.2841 & 32.6955 \\ MLMVN-G-3 & 26.5878 & 31.7009 & 29.6442 & 32.2805 & 32.6411 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of filtering grayscale images affected by additive Gaussian 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.