# A Self-Supervised One-Shot Learning Approach for Seismic Noise Reduction
## 4 Results  
### Additive White Gaussian Noise (AWGN)  
Throughout our experimental investigation, we employed the N2S, N2N, and supervised methodologies to process datasets characterized by varying signal-to-noise ratios (SNRs). The training phases for the N2N and supervised algorithms followed a conventional framework, involving a training set, a separate validation set to monitor and stop training to prevent overfitting, especially in the supervised case that relies on external labels rather than just internal coherence, and a distinct test set to evaluate the efficacy of each method. The dataset was meticulously divided, allocating 770 seismograms to the training set, 330 to the validation set, and 100 to the test set. Alternatively, a one-shot training strategy was adopted for N2S, in which only a single noisy image is considered for model training, resulting directly in the final noise-free image. In both methods, 1000 training iterations were carried out, adopting the \(MSE\) function as a cost function and the Adam algorithm as an optimization strategy with an initial learning rate of 0.0001. We used clean images as a reference; these images were used only for metric calculations and qualitative analysis purposes and were not included in any stage of the training process. In this study, we analyzed different neural network architectures, including a basic FCN3, an FCN9 topology, and the generator component of the super-resolution generative adversarial network (SRGAN--generator). For better comprehension, we categorized the noise levels into three distinct groups: Noise 1, Noise 2, and Noise 5, corresponding to signal-to-noise data ratios of 1, 2, and 5, respectively. Table 1 presents the results of N2S concerning the peak signal-to-noise ratio (PSNR) across the three distinct architectures for these specified noise categories. Our analysis shows that the three architectures we tested, all running on V100 NVLink 8 GPUs, have similar performance outcomes. However, the processing time of the FCN3 architecture stands out, at more than five times faster than the FCN9 architecture and nearly three times faster than the SRGAN generator, as indicated in Table 2. This difference is crucial because it shows that FCN3 not only works well but does so much more efficiently, saving significant time and computational resources. For the qualitative analysis in question, a seismic sample from the test dataset used in the N2N method was chosen, with the addition of Noise 2. Figure 5 displays the three components of this sample: the noisy data, incorporating Noise 2; the original, already cleaned data; and the isolated noise, derived from the subtraction between the noisy and clean data. \begin{table}
\begin{tabular}{c c c c} \hline  & **FCN3** & **FCN9** & **SRGAN—Generator** \\ \hline
**Noise 1** & 52.79 \(\pm\) 0.73 & 53.03 \(\pm\) 1.33 & 52.23 \(\pm\) 0.61 \\
**Noise 2** & 55.68 \(\pm\) 0.92 & 55.28 \(\pm\) 1.67 & 55.62 \(\pm\) 0.75 \\
**Noise 5** & 58.64 \(\pm\) 1.30 & 56.90 \(\pm\) 1.70 & 56.55 \(\pm\) 2.25 \\ \hline \end{tabular}
\end{table} 
Table 1: Average PSNR Values Analysis for Seismic N2S with 100 Shots. The results for this sample are displayed in Figure 6. Each row of the figure corresponds to a tested topology. The left column shows the predicted clean data, and the right column presents the isolated noise obtained by the difference between the noisy data and the prediction. We adjusted the image scale to the 99 th percentile to improve clarity and maintain consistency in visualization. Detailed analysis reveals that all the tested architectures can attenuate the noise present in the data; however, the distortion of the original signal varies. Specifically, the FCN9 architecture produces more pronounced interference in the original signal, whereas the FCN3 and the SRGAN generator architectures have less significant impacts.