## 4 Discussion
In the high-energy case, the standard deviation in MAPE is 4.9%, 3.4%, and 2.6% for single-energy, 1-output, and 2-output dual-energy models, respectively, and the deviation in the relative error is 1.8% for the single-energy network, 1.4% for the 1-output dual-energy algorithm, and 1.1% for the 2-output-dual-energy algorithm. In the low-energy case, the standard deviation in MAPE is 6.0%, 4.1%, and 6.3% for the single-energy, 1-output, and 2-output dual-energy models, and the corresponding values in the relative error are 2.0%, 1.5%, and 2.2%, respectively. All these results point to the superior performance of the dual-energy models for scatter correction of CXRs, being more accurate in the 1-output model for low-energy acquisitions and the 2-output model for high-energy images. The application of the single-energy model to real CXRs acquired without an anti-scatter grid suggests that the algorithm can be easily adapted to be used with true data acquired with different setups since, in this case, the information of the parameters with which the projections were taken was not available in the anonymized Dicom headers used. Furthermore, the accuracy of the model applied to these images could not be quantitatively determined as there was no access to ground-truth, scatter-free CXRs. However, Figure 10 shows that the estimations are robust, even for radiography with artifacts such as wires, as it happens in the third case of this Figure. This is a key aspect, as the application of these models can be especially useful for critically ill patients with whom it is more difficult to utilize an anti-scatter grid (as explained in Section 1). In addition, the values of the ratio between the regions of the lung with and without ribs (Table 2) point out that the scatter correction improves the contrast between different tissues. The two dual-energy models could not be verified against real data since we currently do not have access to CXRs acquired with two different X-ray kilovoltages. Nevertheless, it is expected that good estimations of scatter-corrected images can be obtained in actual images, in light of the results shown in Sections 3.1 and 3.3. Moreover, the superior accuracy shown by the 1-output and 2-output dual-energy models when evaluating the MAPE and the relative error, which has been previously discussed in this Section and in Section 3.1, would be worth studying in future research with real CXRs acquired without an anti-scatter grid with two different energy spectra. This way, it could be determined if dual-energy approaches truly provide better scatter correction, and the gain in DES images after scatter correction could also be tested. [PERSON] and [PERSON] [9] performed a similar study on CXR scatter correction using CNNs and Monte Carlo simulations to generate training cases. They evaluated the SSIM, among other metrics, obtaining an average value of 0.992. This is in the same order as the 0.997 value yielded by the models herein proposed, with ours 0.5% better. As stated by these authors [9],the application of deep learning to scatter correction of CXR has only recently started, so there are not many studies with which results can be compared. Some literature on scatter correction (or estimation) on cone-beam CT images can be found. [PERSON] et al. [13] presented a scatter estimation method based on a deep-learning approach, helped by bivariate B-spline approximation. For thorax CT, the MAPE ranges approximately from 3% to 20% for the five-fold cross-validations, while our models obtain average values of 11.2% and 8.6%. Additionally, the SSIM for the thorax CT study is between 0.96 and 0.99. Although CT and CXR have some obvious differences, and they are not exactly comparable, it can be noticed that our models present a similar precision. The models displayed in this paper still have some limitations that would need further study. First, we uniquely employed simulated images for the training and validation, as well as for the test cases in Section 3.1.