## 4 Discussion  
In this work, we have implemented and evaluated the performance of three deep-learning models that estimate and correct the scatter in CXRs. One model is based on standard single-energy acquisitions, while the other two models assume that two CXRs with different energies (dual energy) were acquired per patient. The impact of varying the distance of the X-ray source on the accuracy of the scatter correction with these methods was studied. Results in Figure 8 demonstrate that the three deep-learning-based models are able to accurately estimate and correct scatter contribution to simulated CXRs. Moreover, the three algorithms keep their accuracy on scatter correction when the source-to-detector distance (SDD) varies in a range of 100 cm from the SDD used to train the neural networks. Thus, the results prove that the models are robust to variations on the setup parameters, such as air gap or SDD, and their application is not limited to a specific configuration. The highest decrease in accuracy is found in SDD = 100 cm and SDD = 200 cm (the neural networks were trained with SDD = 180 cm). For SDD = 100 cm, this result could be expected since it is the case with the largest distance with respect to the reference SDD. The fact that less accurate metrics are obtained for SDD = 200 cm, which is the second closest \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & **C1** & **C2** & **C3** & **C4** & **C5** & **C6** & **C7** & **C8** & **C9** & **C10** & **Avg** \\ \hline Original & 2.71 & 1.66 & 1.36 & 1.11 & 1.35 & 1.16 & 1.71 & 1.47 & 1.28 & 1.59 & 1.54 \\ Scatter-corrected & 3.80 & 2.02 & 1.54 & 1.17 & 1.49 & 1.23 & 2.14 & 1.68 & 1.41 & 1.64 & 1.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Ratio between a region of the lung with and without rib in the original, real CXRs and in the scatter-corrected CXRs yielded by the single-energy algorithm for the 10 CXRs taken as test set (listed as C1–C10), and the resulting average value. Figure 10: Original CXR (with scatter) with pixel value conversion (**left**); estimation of the scatter-corrected CXR (**center**); and estimation of the scatter contribution on real CXR (**right**) of three of the real chest X-ray images used to test the single-energy model of scatter correction. distance to the one of reference, indicates that the models are more accurate if the images are well focused on the lungs and the air-background areas are reduced or cropped. In this case, the lungs become smaller in the image as the SDD increases, which explains the loss of accuracy. According to the mean values of MAPE and relative error shown in Section 3.1, the results obtained with the dual-energy NN models are more accurate than the ones provided by the single-energy model. In the estimations of the scatter-corrected high-energy CXRs, the p-value between the metrics yielded by the 2-output dual-energy and the single-energy models is \(p=4.2\times 10^{-13}\) for the MAPE, and \(p=0.01\) for the relative error, i.e., in both metrics the p-value is below the classic threshold of 0.05 [56; 57], indicating that the difference is statistically significant. In the low-energy estimations, the p-value between the 1-output dual-energy and the single-energy algorithms is \(p=0.05\) for the MAPE and \(p=0.28\) for the relative error, so the difference is significant only in the first metric. As explained in Section 3.1, the difference in the SSIM is minor. Regarding the MSE, there is not a substantial difference between the three models due to the fact that this is the metric employed as a loss function in the training of the algorithms, so it is minimized in both cases. In the comparison between the two proposed models of scatter correction, it is also observed in Figure 8 that there is less deviation in the values of MAPE and relative error applying the dual-energy model.