## 3 Results
### Simulation Results  
From the simulation data used to obtain Figure 4, graphs are presented where the horizontal axis represents the estimation iterations (_iter_) and the vertical axis represents the MAE in Figure 5. It can be observed that the proposed method achieves the minimum MAE at 9 iterations, while the ML-EM method reaches it at 3 iterations.  
Figure 6 shows the true image, sinogram, and reconstructed images obtained using both methods from the initial calculation with a projection angle \(\Delta\theta\) of 30 degrees. The number of estimation iterations required to obtain each image, and the MAE and SSIM for each image, are presented in the captions of the respective figures.  
Additionally, Figure 7 displays the absolute error distributions, obtained using each method and visualized as images.  
Figure 4: Relationship between projection angle \(\Delta\theta\) and SSIM.  
Figure 3: Relationship between projection angle \(\Delta\theta\) and MAE.  
Figure 5: Relationship between estimation iterations _iter_ and MAE (\(\Delta\theta=30\)).  
Figure 6: Simulation results (\(\Delta\theta=30\)). **Top left**: True image (the black areas: regions outside the head, the grey areas: normal cells, and the white areas: tumor cells). **Top right**: Sinogram created by projection. **Bottom left**: Image reconstructed using the proposed method (_iter_ = 9, MAE = 0.0560, and SSIM = 0.3560). **Bottom right**: Image reconstructed using the ML-EM method (_iter_ = 3, MAE = 0.1223, and SSIM = 0.3934).  
Based on the results above, when considering only normal cells (1408 pixels), the average estimated values were 0.3154 \(\pm\) 0.0005 and 0.4597 \(\pm\) 0.0012 for the proposed and ML-EM methods, respectively, while the true value was 0.31. The MAE for normal cells was 0.0481 \(\pm\) 0.0004 for the proposed method and 0.1500 \(\pm\) 0.0012 for the ML-EM method.  
Furthermore, when considering only tumor cells (16 pixels), the average estimated values were 0.5317 \(\pm\) 0.0051 for the proposed method and 0.6601\(\pm\) 0.0090 for the ML-EM method, with a true value of 1.00. Therefore, the \(\mathrm{T/N}\) ratio was approximately 1.7 and 1.4 for the proposed and ML-EM methods, respectively, and it was expected to be 3.2 in this study.  
In BNCT-SPECT, the accuracy of the pixel values in normal cells is critical. To quantify this, we defined the relative error of the reconstructed image compared to that of the true image, as the \"Average value of normal cells/true pixel value of normal cells\", when only normal cells were extracted. Using this measure, the relative error for the proposed method with the projection data obtained at a 30-degree projection angle was calculated to be approximately 16%. For the ML-EM method, it was approximately 48%. The results are summarized in Table 1.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{\(\Delta\theta\) = 30} & **MAE (Entire** & **SSIM (Entire** & **Average Value** & **MAE (Tumor Cells)** & **Average Value** & **MAE (Normal Cells (=0.31)** & **MAE (Normal Cells)** \\ \hline Proposed & 0.0568 \(\pm\) 0.00021 & 0.3624 \(\pm\) 0.0026 & 0.5317 \(\pm\) 0.0051 & 0.4683 \(\pm\) 0