## 3 Results
### Clinical Study  
For the optimization of the \(\sigma\)-value confirmed in the simulation study, it was applied to the brain T2 WI obtained from the ADNI dataset to examine its applicability to the clinical MR image. In addition, we attempted to prove the superiority of the BM3D algorithm with an optimized \(\sigma\)-value in comparison to conventional noise reduction algorithms. The results of applying the algorithms were quantitatively evaluated by comparing the CNR and CV from the perspective of noise level due to the unavailability of a noise-free  
Figure 5: The results of (**a**) contrast-to-noise ratio and (**b**) coefficient of variation for a simulated brain T2-weighted image with respect to the \(\sigma\)-value of the BM3D algorithm. The blue circle represents the important value according to \(\sigma\)-value.  
Figure 6: The results of (**a**) structural similarity index measurement and (**b**) root mean square error for a simulated brain T2-weighted image in accordance with the \(\sigma\)-value of the BM3D algorithm. The blue circle represents the important value according to \(\sigma\)-value.  
reference image in clinical experiments. Figure 10 shows the resulting images for each applied algorithm.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Noise Level 0.05** & \multicolumn{2}{c}{**Noise Level**} & \multicolumn{2}{c}{**Similarity**} \\ \hline  & **CNR** & **COV** & **SSIM** & **RMSE** \\ \hline Gaussian & 15.17 & 0.2980 & 0.3858 & 0.1772 \\ Median & 28.00 & 0.0432 & 0.6500 & 0.1464 \\ Wiener & 34.02 & 0.0352 & 0.6748 & 0.1494 \\ Optimized BM3D & 182.99 & 0.0061 & 0.6974 & 0.1499 \\ \hline \end{tabular}
\end{table}
Table 1: The results of quantitative evaluation of applying Gaussian filter, median filter, Wiener filter, and the optimized BM3D algorithm for each noise level.  
Figure 7: The results of applying (**a**) Gaussian filter, (**b**) median filter, (**c**) Wiener filter, and (**d**) optimized BM3D algorithm to an image with 0.05 Rician noise.  
The CNR values were approximately 34.99, 24.65, 25.26, and 39.74 when the Gaussian, median, Wiener filters, and optimized BM3D algorithms were applied, respectively. The calculated CV values were approximately 0.0102, 0.0151, 0.0148, and 0.0086, respectively. Figure 11 shows a graph of the CNR and CV measured from the images obtained using conventional noise reduction algorithms and the optimized BM3D algorithm.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Noise Level 0.10** & \multicolumn{2}{c}{**Noise Level**} & \multicolumn{2}{c}{**Similarity**} \\ \hline  & **CNR** & **COV** & **SSIM** & **RMSE** \\ \hline Gaussian & 15.42 & 0.0307 & 0.3661 & 0.1931 \\ Median & 20.39 & 0.0570 & 0.5540 & 0.1649 \\ Wiener & 20.47 & 0.0531 & 0.5876 & 0.1689 \\ Optimized BM3D & 142.39 & 0.0080 & 0.6628 & 0.1667 \\ \hline
**Noise Level 0.15** & \multicolumn{2}{c}{**Noise Level**} & \multicolumn{2}{c}{**Similarity**} \\ \hline  & **CNR** & **COV** & **SSIM** & **RMSE** \\ \hline Gaussian & 15.00 & 0.0329 & 0.3491 & 0.2178 \\ Median & 10.60 & 0.0900 & 0.4755 & 0.1924 \\ Wiener & 11.16 & 0.0868 & 0.5094 & 0.1984 \\ Optimized BM3D & 69.34 & 0.0127 & 0.6206 & 0.1940 \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._  
Figure 8: The results of (**a**) contrast-to-noise ratio and (**b**) coefficient of variation for comparison between conventional noise reduction algorithms and the optimized BM3D in the simulation study.  
Figure 9: The results of (**a**) structural similarity index measurement and (**b**) root mean square error for comparison between conventional noise and the optimized BM3D algorithms.  
Figure 10: (**a**) The original ADNI image with an enlarged region for the observance of changes as algorithms and the resulted images after applying (**b**) Gaussian filter, (**c**) median filter, (**d**) Wiener filter, and (**e**) the optimized BM3D algorithm.