# Monte-Carlo-Based Estimation of the X-ray Energy Spectrum for CT Artifact Reduction
## 4 Conclusions  
In this study, a validated Monte Carlo simulation-based approach was proposed to calculate the X-ray energy spectrum of a flexible X-ray scanner for CT artifact reduction applications. Firstly, both the X-ray tube and flat panel detector of the FleXCT scanner were completely modeled, after which the X-ray spectrum was calculated inside the flat panel detector for different tube voltages. In order to validate the modeled system by Monte Carlo simulation, the MLEM method was implemented to estimate the spectrum of the X-ray source based on empirical transmission data. To provide the required data for the MLEM method, a PVC step wedge was scanned (tube voltage between 60 and 200 kV). In order to mimic a parallel X-ray beam, the step wedge was positioned as close as possible to the detector and the flat panel detector further downstream, optimally exploiting the flexibility of the FleXCT system. Within each step wedge, a region of interest was cropped,  
Figure 11: (**a**) A slice of the steel cylinder reconstructed by the Simultaneous Iterative Reconstruction Technique (SIRT). (**b**) A slice of the steel cylinder reconstructed by Polychromatic SIRT (PSIRT). (**c**) Gray value intensity line profile along the central horizontal line of the reconstructed slices using SIRT and PSIRT.  
after which its mean value was used for the MLEM calculations. The product of the X-ray spectrum for each tube voltage with the normalized absorption response function of a GadOx scintillator (obtained by Monte Carlo simulation) was used as an initial guess for the MLEM calculations. A good correlation between results of the Monte Carlo simulation and the MLEM method (RMSE value of 0.0046) confirmed the correct modeling of the FleXCT system by the Monte Carlo simulation technique. After validating the simulation geometry of the FleXCT system, the required X-ray energy spectrum was calculated in front of the X-ray tube, which is a prerequisite for beam hardening and scattering CT artifact reduction applications. As a proof of principle, the FleXCT X-ray energy spectrum was calculated for a tube voltage of 230 kV and then applied to beam hardening artifact reduction of a printed steel cylinder.  
The proposed method can be applied to every medical and industrial X-ray imaging system as a trustable method for calculating the X-ray energy spectrum.  
Conceptualization, E.N., N.S., J.S. and J.D.B.; methodology, E.N. and N.S.; investigation, E.N., N.S., D.I., B.D.S., J.S. and J.D.B.; writing--original draft preparation, E.N., N.S. and D.I.; writing--review and editing, E.N., N.S., D.I., B.D.S., J.S. and J.D.B.; supervision, J.S. and J.D.B.; funding acquisition, J.S. and J.D.B. All authors have read and agreed to the published version of the manuscript. Funding for the FleXCT scanner was provided by grant no. I002718N from the research foundation Hamders (FWO Vlaanderen). This work is financially supported by the VLAIO ICON project VIL (HBC.2019.2808), the FWO SBO projects S003421N and S004217N and FWO fellowship 11D8319N. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data is contained within the article. We acknowledge Smart*Light funded by the Interreg V Flanders-Netherlands program with financial support from the European Regional Development Fund (ERDF). Conflicts of Interest: The authors declare no conflict of interest.