## 3 Results
### Batch Size and the Learning Results
As part of our experiments, we trained several MLMVN models to filter additive Gaussian noise and speckle noise. As was already mentioned, we employed the MLMVN topology 64-1024-64 because it has shown the best results. This topology processes 8 \(\times\) 8 image patches in the frequency domain. MLMVN-G-1, MLMVN-G-2, and MLMVN-G-3 were trained for denoising images with additive Gaussian noise, while MLMVN-S-1, MLMVN-S-2, and MLMVN-S-3 were trained for denoising images with multiplicative speckle noise. In all MLMVNs neurons in the hidden layer employed a standard continuous MVN activa \begin{table}
\begin{tabular}{c c c c c c} \hline \hline Number of samples in a batch & Train station & Music hall & Big Ben & Cambridge bldg & Gaudi bldg \\ \hline
1000 & 29.8493 & 29.2612 & 27.1164 & 29.9298 & 28.7228 \\
2000 & 29.6757 & 29.3202 & 26.9995 & 30.0297 & 28.8767 \\
3000 & 29.6286 & 29.2861 & 27.0174 & 30.0147 & 28.8323 \\
4000 & 30.1186 & 29.5799 & 27.3663 & 30.207 & 29.1725 \\
5000 & 30.2527 & **29.621** & 27.4764 & 30.1601 & **29.2054** \\
6000 & 30.2331 & 29.6 & 27.4192 & **30.244** & 29.1891 \\
10,000 & **30.4166** & 29.6002 & **27.5986** & 30.0765 & 29.128 \\
20,000 & 29.8485 & 29.3861 & 27.3098 & 30.1236 & 28.9371 \\ \hline Number of samples in a batch & Barcelona Plaza & Sailboat & Manhattan & Airplane & Fisher-jet \\ \hline
1000 & 28.3432 & 33.3609 & 31.4869 & 33.7677 & 33.9199 \\
2000 & 28.4496 & 33.6422 & 31.63 & 34.0288 & 34.2254 \\
3000 & 28.4347 & 33.5338 & 31.5108 & 33.7992 & 34.2069 \\
4000 & 28.6853 & 33.8204 & 31.8179 & 34.4496 & 34.448 \\
5000 & 28.717 & 33.8101 & 31.8114 & 34.3776 & 34.5142 \\
6000 & 28.7273 & **33.8849** & **31.876** & **34.5031** & **34.5963** \\
10,000 & **28.7651** & 33.5517 & 31.7046 & 34.1539 & 34.4115 \\
20,000 & **28.5961** & 33.1434 & 31.3268 & 33.4583 & 33.9033 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The PSNR of the noisy images (additive Gaussian noise with SD = 0.2\(\sigma\)) from the test dataset processed by MLMVN trained using different batch sizes. The best results are highlighted in bold. Figure 6: Effect of an activation function: (**a**) a standard continuous activation function for MVNs; (**b**) the complex-valued sigmoid activation function; (**c**) the complex-valued hyperbolic tangent activation function. Red crosses represent MVN weighted sum values and blue circles represent respective neuron outputs after applying a respective activation function to the weighted sums. tion function. The output layers of MLMVN-G-1 and MLMVN-S-1 employed the identity activation function, MLMVN-G-2 and MLMVN-S-2 employed the complex-valued sigmoid activation function, and MLMVN-G-3 and MLMVN-S-3 employed the complex hyperbolic tangent activation function. Figure 7 shows convergence curves for all these MLMVN models. These curves represents the mean PSNR over the validation set vs. the number of epochs/batches. Figure 7: Convergence curves. The mean PSNR over the validation set during the learning process, measured after learning of each batch is completed: (**a**) MLMVN-G-1, (**b**) MLMVN-G-2, (**c**) MLMVN-G-3, (**d**) MLMVN-S-1, (**e**) MLMVN-S-2, (**f**) MLMVN-S-3. The notation E: X, B: Y denotes Epoch X and Batch Y.