## 4 Discussion  
The importance of noise reduction algorithms for medical imaging is significantly increased. Therefore, the appropriate parameters are considered as a key to acquire reasonable image quality for diagnosis [34; 35; 36]. The performance of the BM3D algorithm is influenced by various modifier factors; however, among them, \(\sigma\)-value is a factor that determines the degree of smoothing of the signal values and serves as a criterion for discriminating and eliminating noise [22]. In this study, we aimed to determine the optimal \(\sigma\)-value of the BM3D algorithm by adjusting the \(\sigma\)-value from 0.01 to 0.99 and applying it to simulated and clinical MR images, thereby attempting to identify the \(\sigma\)-value that could yield the optimal image characteristics. The results of applying the BM3D algorithm to the simulated brain T2 WI acquired using the BrainWeb simulation program were evaluated using quantitative evaluation factors of CNR, CV, SSIM, and RMSE. Quantitative evaluation demonstrated that when the three intensities of Rician noise of 0.05, 0.10, and 0.15 were added, the CNR initially exhibited a sharp increase with an increase in the \(\sigma\)-values up to 0.08, 0.13, and 0.15, respectively. Subsequently, irregular fluctuations without a clear pattern were observed. Similarly, the CV also displayed a rapid decrease until the above-mentioned \(\sigma\)-value, following which it exhibited a minimal difference. Overall, we confirmed that the CNR and CV increased and decreased exponentially up to a certain \(\sigma\)-value for all three noise intensities; however, thereafter, the quantitative evaluation results demonstrated fluctuation patterns that were not consistent. This means that excessive smoothing was achieved by applying a \(\sigma\)-value higher than the noise intensity contained in the image. As a result of the similarity evaluation, both SSIM and RMSE rapidly increased until a certain \(\sigma\)-value and then decreased. The \(\sigma\)-values that exhibited these trends were found to be 0.08, 0.13, and 0.16 for images with Rician noise intensities of 0.05, 0.10, and 0.15, respectively. These values were aligned with the \(\sigma\)-values that showed optimal image characteristics in the assessment of noise-level variations. The images acquired using the BrainWeb simulation program and the T2 WI from the ADNI dataset are obtained using different methods. In particular, the T2 WIs from the ADNI dataset are actual clinical images with unknown noise distribution. Despite this, the reason why the optimized sigma value derived from the simulation study could be applied is that the additional noise introduced during the simulation study was modeled as Rician noise, considering that MR signals exhibit a complex form. Rician noise distribution is similar to the noise encountered in clinical settings; there are practical limitations in measuring and applying the noise distribution of each acquired image. Therefore, the  
Figure 11: The results of the (**a**) contrast-to-noise ratio and (**b**) coefficient of variation in the optimized BM3D and conventional noise reduction algorithms. final optimized sigma value of 0.12 was derived as the average of the sigma values that demonstrated excellent quantitative evaluation results at various levels of additional noise in the simulation study. As a result, we consider that this optimized sigma value maintains consistency even in a blind state of noise estimation. Clinical MR images of brain T2 WIs were obtained from the ADNI dataset. The BM3D algorithm with a \(\sigma\)-value of 0.12 was obtained from the simulation study and applied to confirm its usability. We attempted to compare and evaluate the performance by applying conventional noise reduction algorithms: Gaussian, median, and Wiener filters. Consequently, the CNR and CV were calculated as 39.74 and 0.0086, respectively, when the optimized BM3D algorithm was applied.