## 2 Method
### Dataset Acquisition  
The dataset utilized in this study was obtained through analytical simulation, taking into account results from our previous research [23]. Multispectral X-rays with energy spectrum \(\Omega(E)\) can be subdivided into smaller energy bins based on their energy levels, with photons within each bin having similar energies and approximately obeying the Lambert-Beer law. The material's response to multispectral X-rays is the cumulative integration of responses from all energy bins. Given that the spectrum of the X-rays and the attenuation coefficient \(\mu_{E,S}\) are known, the relationship between the incident X-ray intensity \(I_{input}\) and the transmitted intensity \(I_{output}\) can be represented by the following equation:  
\[I_{output}=I_{input}\int\Omega(E)e^{-\int\mu_{E,S}dS}dE\]  
In this way, a projection process of CT analytical simulation is transformed into a process of segmenting X-ray beam energy intervals, determining the types of substances, and calculating the attenuation coefficient of the substance in a given energy interval during the path attenuation. The X-ray energy spectrum of tungsten target material at an acceleration voltage of 260 KeV is shown in Figure 2, generated by SpekCalc (v.2009) software [24]. According to the simulation requirements, the X-ray energy spectrum is segmented into 30 energy zones. In the simulation calculation process, it is assumed that photons within an energy zone have the same energy, and the total number of photons in the energy zone can be calculated based on the proportion of that energy zone. The transverse slice of the phantom in Figure 3 is illustrated and the principle of industrial fan-beam CT is shown in Figure 4. In the simulation process, the size and spatial position of pixels determine the path length of X-ray penetration. Different grayscale values represent different materials. Data from the cross-section library are called based on material numbers to calculate the cumulative factor of the interaction between X-rays and substances in the attenuation path. Figure 2: Energy spectrum of X-ray tube at 260 KeV. Assume that photons in each energy bin have the same energy during the simulation. Artifacts caused by beam hardening, scattering, and noise are approximately simulated based on this principle. During the calculation of the cumulative factor, it is essential to have cross-sectional data for different material compositions and X-ray interactions at a given energy level. With the increasing depth of research on the interaction between X-rays and substances, more research units have access to accurate experimental and theoretical cross-sectional data. The cross-sectional database used originates from the X-ray Cross Sections Database (XCOM), developed by the National Institute of Standards and Technology of the United States. It covers cross-sectional data of X-ray interactions with substances up to 300 KeV, commonly used in our industrial micro-focus CT. This database provides a wide range of material types and their cross-sectional data, and also supports the calculation of compound cross-sections in different proportions. Our designed MATLAB(R2021b)-CUDA 11.3 hybrid program can rapidly retrieve cross-sectional data for specified materials and energies by accessing the XCOM database, along with the proportion of the total number of photons in that energy range to the overall photon share. Figure 4: Schematic diagram of the working principle of fan-beam CT.  
Figure 3: The slices of the scanned object correspond to different materials with varying grayscale values. During the simulation process, the cross-sectional data from the XCOM database are called based on the corresponding materials. In the simulation process, the materials of the scanned objects included metals such as Fe, Al, alloy steel, and aluminum alloy.