## 2 Materials and Methods
### Image Quality Evaluations  
To quantitatively evaluate the image quality according to the projection angle and filter changes in the FDK algorithm, we calculated the coefficient of variation (COV), signal to noise ratio (SNR), root mean square error (RMSE), universal image quality index (UQI), and blind/referenceless image spatial quality evaluator (BRISQUE) [25, 26, 27, 28, 29]. We used MATLAB  
Figure 1: Slice selection in the cone beam computed tomography (CBCT) reconstruction image.  
(ver. 2023a; MATHWORKS, Boston, MA, USA) to calculate the quantitative evaluation factors. We selected the 170 th slice from the reconstructed 3D volume data, ensuring that it included the air, brain, and bone regions, to measure various quantitative evaluation metrics based on selected 2D images. Figure 2A shows the regions of interest (ROIs), indicating the material regions, including air, brain, and bone, for noise level evaluation in yellow boxes. The red box indicates the magnified region for visual evaluation in Figure 2A, and Figure 2B shows a reference image for similarity evaluation.  
To evaluate the noise level in the reconstructed image based on the filters and projection angle, ROIs were set in the air, brain, and bone regions to calculate the COV and SNR. The COV is useful for comparing the degree of change between different sets of data, even when their means are different, and is defined as the ratio of the standard deviation \(\sigma\) to the mean value \(\mu\) (Equation (8)). SNR is the signal intensity of the region of interest compared to the noise signal, indicating the relative magnitude of the signal, where \(S_{A}\) and \(\sigma_{A}\) represent the mean and standard deviation of the region of interest (Equation (9)):  
\[COV=\frac{\sigma}{\mu} \tag{8}\]  
\[SNR=\frac{S_{A}}{\sigma_{A}} \tag{9}\]  
The standard deviation and mean value for each ROI were calculated from a 20 \(\times\) 20 matrix size for air, brain, and bone in the phantom image (Figure 2).  
To evaluate the similarity of the FDK reconstruction algorithm using various filters and projection angles, we acquired reconstructed images of noise-free projection data scanned at a projection angle of 0.01\({}^{\circ}\), the minimum angle possible for simulation program, as a reference image. We used the Hann filter as the reconstruction filter, which has demonstrated superior performance in noise level evaluations in previous studies [17]. The RMSE and UQI of the acquired reference and noisy reconstructed images were calculated. A smaller RMSE value indicates less error between the original and reference images, and a UQI value closer to 1.00 signifies a higher similarity in the intensity of the two image signals.  
\[RMSE=\sqrt{\frac{\sum_{i=1}^{N}(f_{i}-g_{i})^{2}}{N}} \tag{10}\]  
Figure 2: (**A**) Acquired image with regions of interest (ROIs) for noise evaluation and (**B**) reference image for similarity evaluation.  
\[UQI=\frac{4\mu_{f}\mu_{g}\sigma_{fg}}{\left(\mu_{f}^{2}+\mu_{S}^{2}\right)\left( \sigma_{f}^{2}+\sigma_{S}^{2}\right)} \tag{11}\]  
where \(f\) and \(g\) represent the reference and comparison images, respectively, and \(N\) represents the number of pixels in the image. The mean luminance values are represented by \(\mu_{f}\) and \(\mu_{g}\), and \(\sigma_{fg}\) represents the covariance between the two images.  
We used BRISQUE--an algorithm that evaluates the spatial quality of an image without a reference image--as the blind quality assessment method. BRISQUE measures the level of distortion by analyzing image quality characteristics related to visual perception. BRISQUE can identify spatial quality issues such as noise and blur, and considers the relationship between recognizability and subjective quality, with a lower value indicating higher image quality [29; 30].