# A Self-Supervised One-Shot Learning Approach for Seismic Noise Reduction
## 4 Results
### Real Noise  
In the case of real noise, the lack of different realizations of the same seismic shot makes testing and using the N2N method impracticable, as its application directly depends on two samples of the same image. However, the proposed method, which uses the image itself for training, can be applied for analysis. Tests were carried out using the same hyperparameters used in the Gaussian noise optimization, with equivalent cost functions and preprocessing involving mean and standard deviation.  
For the implementation in question, we opted for the FCN3 and the SRGAN generator topologies. These were selected on the basis of their superior performance in tests involving Gaussian noise. This decision was balanced against consideration of the evaluation metrics, required processing time, and minimal signal removal. To evaluate and compare the effectiveness of our proposed method, we implemented the supervised method using the same topologies employed in the N2S method.  
In our experiments, we noticed that convergence was achieved with fewer epochs, which prompted us to limit the total number of iterations to 500. This decision resulted in a processing time of approximately 6.8 min for the FCN and 39.5 min for the SRGAN, maintaining the same configuration as that used for the Gaussian noise experiments. The  
Figure 8: Average PSNR performance over 100 shots across epochs with FCN3 and SRGAN generator topologies—Noise 2.  
Figure 7: Comparison of synthetic data utilizing Noise 2: (**a**) raw data; (**b**) noise-reduced data from N2S; (**c**) noise-reduced data from N2N; and (**d**) noise-reduced data from the supervised method.  
outcomes from analyzing 100 seismic records affected by real noise for both topologies are detailed in Table 4.  
For the qualitative analysis presented, we used the same seismic sample from the test dataset as that previously analyzed but incorporated real noise. Figure 9 illustrates the following elements: the noisy image, the clean (original) image, and the noise derived from the difference between the original and clean images.  
Figure 10 shows the predictive results obtained by the proposed model in comparison with those of the supervised model. The first row shows the results for the FCN3 topology for both models, including the respective differences. The second row presents analogous results for the SRGAN generator topology. Like the results obtained with Gaussian noise, the intensity scale shown was determined on the basis of the 99 th percentile of the intensity distributions, thereby ensuring consistent and informative visualization of the analyzed data.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Topology** & **N2S** & **Supervised** \\ \hline FCN3 & \(56.06\pm 0.74\) & \(81.32\pm 1.97\) \\ SRGAN—Generator & \(47.47\pm 0.78\) & \(78.61\pm 1.83\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Average \(PSNR\): synthetic seismic data with real noise added (100 shots).  
Figure 9: Shot gather records (real noise).  
Although the results from the FCN3 network are inferior to those of the supervised method (Table 4), qualitative analysis indicates that the FCN3 network manages to remove most of the noise, suggesting its effectiveness in this process (Figure 9). However, a slight increase in the loss of useful signal is observed, particularly compared with the results obtained in Gaussian noise scenarios, which justifies the worse quantitative results. Considering the use of a single image for training, the topology performance is deemed satisfactory.  
In contrast, the SRGAN generator performance does not meet our expectations. This model tends to excessively remove signals, significantly diminishing the overall image quality compared with that of the original recordings. This suggests that more complex architectures may affect the original signal more severely, resulting in a reduction in image quality.