## 2 Test Objects and Methods
### Specific Features of the Variation of the X-ray CT System Parameters  
The goal of this research is to find ways to reduce metal artifacts by varying the parameters of the X-ray CT systems. The main variable parameters of X-ray CT systems are: the maximum energy of X-ray radiation \(E_{\max}\); the effective atomic number \(Z_{f}\) and the mass thickness of the preliminary filter \(\rho h_{f}\), and the ADC bit depth \(k_{\rm ADC}\) for the integral mode of registration.  
It was noted above that reduction of metal artifact levels in X-ray CT is achieved by: increasing the maximum energy of X-ray radiation [7; 11]; stiffening the X-ray beam due to its pre-filtering [9; 10; 11]; matching the variation ranges of the original analog and digital signals with respect to the integral mode of photon registration through the rational choice of ADC bit depth or narrowing the variation range of the primary analog signals [42].  
Limitations associated with the choice of a pre-filter are associated with a decrease in the number of photons hitting the frontal detector surfaces, which leads to an increase in the effect of \"photon (quantum) starvation\" [11] and the necessity to increase the integration time.  
In a number of cases, insufficient ADC bit depth causes the effect of \"pseudo-quantum starvation\" in digital radiography and X-ray CT [43] and leads to the appearance of metallic artifacts in the reconstructed images. The limitations associated with ADCs are due to the availability of fast ADCs with the required bit depth on the market for scientific equipment or preamplifiers that narrow the range of analog signals.  
It is known that increasing the maximum energy \(E_{\max}\) of X-rays leads to an increase in the energy \(I_{ab}\) absorbed in the TO during the formation of projections. It is not the absolute value of absorbed energy that is of interest, but the degree of its increase \(k_{ab}\) in comparison with the base value of maximum energy \(E_{\max 0}\).  
Regardless of the registration mode, the formula for estimating \(I_{ab}\) (\(E_{\max}\)) is as follows  
\[I_{ab}(E_{\max})=N_{0}(E_{\max})\int\limits_{0}^{2\pi}\int\limits_{-R}^{R}\int \limits_{0}^{E_{\max}}Ef_{N}^{**}(E,E_{\max})\int\limits_{L(\theta,x^{\prime} )}\int\limits_{0}^{y^{\prime}}\exp(-m(E,Z(x^{\prime},y^{\prime}))\rho(x^{ \prime},y^{\prime})\mathrm{d}y^{\prime})\frac{m_{ab}(E,Z(x^{\prime},y^{\prime }))}{m(E,Z(x^{\prime},y^{\prime}))}dy^{\prime}dE\mathrm{d}\theta\mathrm{d}x^{ \prime}, \tag{20}\]  
where \(m_{ab}(E,Z(x^{\prime},y^{\prime}))\) is the mass absorption coefficient of photons with energy \(E\) at a point with coordinates \((x^{\prime},y^{\prime})\); \(f_{N}^{**}(E,E_{\max})\) is the energy spectrum of a pre-filtered radiation source.  
In accordance with the definition given above, the dependence of the degree of increase in absorbed energy \(k_{ab}\) when the maximum energy \(E_{\max}\) changes is described by the expression  
\[k_{ab}(E_{\max},E_{\max\ \ 0})=I_{ab}(E_{\max})/I_{ab}(E_{\max\ 0}). \tag{21}\]  
Evaluation of the \(k_{ab}\) parameter will judge the admissibility of increasing the maximum energy of X-rays in order to reduce metal artifacts in X-ray CT.