## 5 Conclusions  
In this work, we presented three deep-learning-based methods to estimate the scatter contribution in CXRs and obtain scatter-corrected projections: a single-energy model, with one input and one output image; a 1-output dual-energy model, in which a projection acquired with a different energy spectrum is set as an additional input channel, but the output has only one channel; and a 2-output dual-energy model, in which the scatter estimation is provided for the two energies introduced in the two input channels. The three models were robust to variations in the SDD, obtaining a high precision for distances in a range between 100 and 200 cm and proving that a similar accuracy with respect to images with the original SDD of the training data (SDD = 180 cm) can be maintained. Moreover, the contrast values between the lung region affected by COVID-19 and the healthy region in soft-tissue images (obtained by means of dual-energy subtraction) demonstrated that scatter correction in CXRs provides better contrast to the area of the lesion, yielding a PCIF of up to 20.5%.  
In both studies (accuracy in scatter correction for several SDD and contrast value in COVID-19 region), the dual-energy algorithms provide results with better accuracy. The analysis of the p-value demonstrates that the difference in accuracy between the single-energy and dual-energy models can be statistically significant, especially in the scatter-corrected estimations of high-energy CXRs with the 2-output method. The single-energy algorithm is accurate enough for scatter correction of CXRs, so it might not be worth acquiring an extra CXR just for this purpose. However, dual-energy models are proven to be a useful tool for scatter correction on soft-tissue DES CXRs.  
The single-energy model was tested with a cohort of real CXRs acquired without an anti-scatter grid, yielding robust, qualitative estimations of the scatter correction, even for images with artifacts. Further studies with real phantoms and patients should be performed to quantitatively determine the precision of the three models with real data and analyze whether the difference between the performance of the single- and dual-energy algorithms is relevant.  
Conceptualization, C.F., J.L.H. and J.M.U.; Methodology, C.F., J.L.H. and J.M.U.; Software, C.F., F.A.-V., P.L., G.M. and A.V.-A.; Formal Analysis, C.F.; Investigation, C.F., J.L.H. and J.M.U.; Writing--Original Draft Preparation, C.F.; Writing--Review & Editing, (all authors); Visualization, C.F.; Project Administration, J.L.H. and J.M.U.; Funding Acquisition, J.L.H. and J.M.U. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the Spanish Ministry of Science and Innovation grant numbers PID2021-126998 OB-I00, RTC2019-007112-1 XPHASE-LASER and PDC2022-133057-I00/AEI/10.13039/501100011033/Union Europea NextGenerationEU/PTR grants. [PERSON] work was funded by a University Complutense of Madrid and Banco Santander predoctoral fellowship, CT82/20-CT83/20.  
**Data Availability Statement:** The simulated CXR dataset and the neural networks code is publicly available at [[https://github.com/clarafreijo/CXR-Scatter-Correction](https://github.com/clarafreijo/CXR-Scatter-Correction)]([https://github.com/clarafreijo/CXR-Scatter-Correction](https://github.com/clarafreijo/CXR-Scatter-Correction)) (accessed on 4 December 2023).  
**Conflicts of Interest:** The authors declare no conflict of interest.