## 2 Materials and Methods  
### Image Reconstruction  
The FDK reconstruction algorithm was used because of its simple implementation and low computational requirements [20; 21]. The FDK algorithm is one of the most referenced methods and a widely used approximation for CBCT reconstruction using circular trajectories. Based on a filtered backprojection method, the FDK reconstruction algorithm provides the flexibility to work with incomplete scan positions while maintaining high computational efficiency. The reconstruction image is generated by initially applying geometric coefficients to weight the projection data, thereby generating a weighted projection function. Subsequently, the weighted projection data is convolved with a selected filter \(f\), and the filtered data is finally backprojected at various angles using the formula outlined in Equation (1):  
\[g(t,s)=\frac{1}{2}\int_{0}^{2\pi}\frac{D^{2}}{(D-s)^{2}}\int_{-\infty}^{\infty }P_{a}(p,\varepsilon)f\bigg{(}\frac{dt}{D-s}-p\bigg{)}\times\frac{D}{\sqrt{D^{ 2}+p^{2}+\varepsilon^{2}}}dpda \tag{1}\]  
where \(P_{a}(p,\varepsilon)\) is the projection data of an object \(f(x,y,z)\) obtained at angle \(a\), and \(D\) is the distance from the source to the detector. The filter \(f\) is applied using a one-dimensional (1D) method along a line parallel to the source trajectory plane within the detector plane.  
The most appropriate method for studying CT image reconstruction algorithms is to acquire human body images using actual CT equipment. However, there are many limitations to the use of this approach based on research ethics. Therefore, we used the tomographic iterative graphics processing unit-based reconstruction toolbox (TIGRE), which is a CBCT simulation program. TIGRE, the CT simulation tool used in this study, enables users to customize various parameters, such as projection angle, geometry, and phantom, and enables simulated repeated acquisition of images under customized conditions [22]. Therefore, to reconstruct the CBCT images, we used the head phantom included in TIGRE,an open-source program for reconstructing 3D images from projection data. The default head phantom in the TIGRE program is based on a standard brain model and was created to simulate the artifacts and noise that can occur during a CT scan. The CBCT system employed in the simulation features a 512 \(\times\) 512 matrix virtual detector with each pixel set to 0.8 mm. The distance from the source to the detector was set to 1536 mm, and distance from the source to the origin was set to 1000 mm. The size of the reconstructed image was set to 256 \(\times\) 256 \(\times\) 256 mm (the voxels were 512 \(\times\) 512 \(\times\) 512) to obtain 512 slices in the z-axis direction, as shown in Figure 1. In the process of acquiring reconstructed images, Gaussian noise with a mean of 0 and a standard deviation of 0.5 was added to the projection data acquired through the head phantom using the addnoise function built into the TIGRE program to replicate the noise environment under low-dose protocol during actual CT scans [23,24]. For similarity evaluation, we additionally acquired projection data without Gaussian noise to obtain reconstructed images under identical conditions. Subsequently, we evaluated the variations in the quality of the reconstructed images using different projection angles and reconstruction filters, which are parameters of the FDK algorithm.