# A Self-Supervised One-Shot Learning Approach for Seismic Noise Reduction
## 4 Results
### Additive White Gaussian Noise (AWGN)
This suggests that the analyzed architectures exhibit distinctive efficacy in preserving the original signals, with the FCN3 and the SRGAN generator ensuring greater integrity of the clean data than FCN9. To assess the efficacy of the proposed methodology, a comparative study was conducted to compare the proposed method with the traditional self-supervised method, N2N, and a supervised methodology. This study included the three architectures used in the preliminary analysis of both methods. The performance was evaluated with the average PSNR and its standard deviation from a sample of 100 seismic shots. The results obtained with the N2N and supervised methods are presented in Table 3. A comparative analysis with the data from Table 1 reveals that the proposed method achieves slightly lower PSNR values than N2N and the supervised method. However, a significant advantage of the new method is its ability to be trained from a single example, drastically reducing the amount of data needed for its effective operation. This characteristic represents a substantial competitive advantage for the proposed method. In addition to the quantitative analysis, an additional qualitative assessment was performed, as shown in Figure 7. To improve the comparison, a side-by-side depiction of the original noisy data and the predictions generated by the N2S, N2N, and supervised methods is included. The model employed in both methods was FCN3, as it proved to be the most efficient in terms of cost-effectiveness and processing time. The analysis allows visual confirmation of the previously presented quantitative results, with the proposed method demonstrating its effectiveness in noise removal comparable to that of the N2N method. In conjunction with the main analysis, the number of training iterations used when the FCN3 and SRGAN topologies were employed was explored. While the standard number of iterations set for the study was 1000, the effectiveness of the N2S method at an SNR of 2 was also examined across different iterations. Importantly, even with a total of 500 iterations, effective results are observed. Figure 8 demonstrates that the results progressively improve with increasing number of iterations until a stabilization point is reached, where minimal improvement is seen with increasing number of epochs. Thus, the process could be started \begin{table}
\begin{tabular}{c c} \hline
**Topology** & **Time (min)** \\ \hline FCN3 & 14.50 \\ FCN9 & 75.87 \\ SRGAN—Generator & 22.38 \\ \hline \end{tabular}
\end{table} 
Table 2: Process time for N2S Method—1000 iterations. Figure 5: Shot gather records (Noise 2). with a reduced iteration volume, equivalent to half of the standard presented, and there is room for refinement in the model performance. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Model** & **Noise 1** & **Noise 2** & **Noise 5** \\ \hline \multirow{3}{*}{N2N} & FCN3 & \(57.18\pm 1.02\) & \(61.56\pm 1.22\) & \(66.30\pm 1.38\) \\  & FCN9 & \(59.41\pm 1.74\) & \(63.22\pm 2.01\) & \(67.24\pm 1.78\) \\  & SRGAN—Generator & \(58.15\pm 1.15\) & \(62.32\pm 1.49\) & \(67.39\pm 1.71\) \\ \hline \multirow{3}{*}{Supervised} & FCN3 & \(58.00\pm 1.11\) & \(62.04\pm 1.42\) & \(67.28\pm 1.68\) \\  & FCN9 & \(60.03\pm 2.20\) & \(64.14\pm 2.72\) & \(69.17\pm 2.76\) \\ \cline{1-1}  & SRGAN—Generator & \(58.99\pm 1.49\) & \(63.01\pm 1.89\) & \(68.28\pm 2.18\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: \(PSNR\)—Seismic N2N and supervised methods (100 shots). Figure 6: N2S Results: (**a**) Prediction using FCN3 topology; (**b**) comparison between removed noise and data predicted with FCN3; (**c**) prediction using FCN9 topology; (**d**) comparison of removed noise and data predicted with FCN9; (**e**) prediction using SRGAN generator topology; (**f**) comparison between removed noise and data predicted with the SRGAN generator. It is worth noting a slight decrease in PSNR for the FCN3 model between Epochs 1500 and 1750.