## 3 Results  
### Accuracy of Scatter Correction on Simulated CXRs  
An example of high-energy, scatter-corrected estimations of the single-energy model and the 1-output and 2-output dual-energy models are represented in Figure 7 for one of the test cases with SDD = 180 cm, as well as the differences between these estimations and the ground-truth scatter-corrected CXR, which is shown in Figure 1.  
The values of MSE, MAPE, SSIM, and the relative error for the test cases with the original SDD and the ten additional variations are represented with a box plot (Figure 8). The results of the four metrics show that the scatter correction models provide an accurate estimation of the scatter correction for the original source-to-detector distance (SDD = 180 cm), highlighted with a red box. For the high-energy images, the average MSE is in the order of \(7.3\times 10^{-6}\), the MAPE indicates an average precision of 11.2%, 8.6%, and 7.6%, while the relative error presents mean values of 4.8%, 4.0%, and 3.6% for the single, 1-output dual-energy, and 2-output dual-energy models, respectively. Moreover, the average SSIM is 0.997 for the single-energy algorithm and 0.998 for both dual-energy NNs, which demonstrates that the outputs of the models have an elevated structural similarity to ground-truth images. Regarding the scatter correction of low-energy images, the average MSE in the single-energy model is \(2.2\times 10^{-6}\), and \(1.5\times 10^{-6}\) for the two dual-energy networks. The MAPE is 17.1%, 14.0%, and 16.6% for the single-energy, 1-output dual-energy, and 2-output dual-energy models, respectively, while the relative error has average values of 7.3%, 6.7%, and 7.0%. The SSIM obtained in the three models is, on average, 0.999. Comparing the estimations for high-energy and low-energy images, it is observed that the MAPE and the relative error are higher in the models for low-energy scatter correction estimations, but good accuracy is still achieved. In all graphics in Figure 8, it is observed that the mean values of the metrics evaluated over the test cases remain very similar for the different SDDs in relation to the original SDD with which the NNs were trained. In the high-energy estimations, the biggest increase among all the evaluated SDD for the MSE is 22.6% in the single-energy model, 15.5% in the 1-output dual-energy model, and 2.4% in the 2-output dual-energy model. In the MAPE, the greatest deviation from the mean value corresponding to SDD = 180 cm is 7.3%, 10.7%, and 3.9%, respectively. In the SSIM, the differences among the various SDD cases are barely relevant (0.06%, 0.04%, and 0.01%), while the major differences in the relative error are in the same order that the ones in the MAPE (7.6%, 8.6%, and 2.5% for single, 1-output and 2-output dual-energy algorithms, respectively). Similar results are obtained in the low-energy estimations: the major deviations are 3.1%, 14.0%, and 6.3% in MSE; 8.2%, 5.7%, and 9.0% in MAPE; and 4.1%, 4.5%, and 5.7%, for the single-energy, 1-output, and 2-output dual-energy models. Again, variations in SSIM are negligible. In all cases, the biggest deviations with respect to the original SDD are found either in SDD = 100 cm or SDD = 200 cm. Furthermore, graphics in Figure 8 show that the range of the maximum and minimum values of the metrics for the 22 test cases remains much the same in all SDDs in comparison with the original one. Figure 7: **(a) Scatter-corrected image estimated by the single-energy model. (b) Scatter-corrected image estimated by the 1-output dual-energy model. (c) Scatter-corrected image estimated by the 2-output dual-energy model. (d) Difference pixel by pixel between the scatter-corrected ground-truth image (represented in Figure 1) and the scatter-corrected image estimated by the single-energy model. (e) Difference pixel by pixel between the scatter-corrected ground-truth image (represented in Figure 1) and the scatter-corrected image estimated by the 1-output dual-energy model.