## 4 Discussion
In comparison with the original noise-added and conventional noise-reduction algorithms, the optimized BM3D demonstrated substantial improvements in CNR by approximately 1.68, 1.13, 1.61, and 1.57-fold compared with noisy image, Gaussian, median, and Wiener filters, respectively. Additionally, the optimized BM3D demonstrated the best performance in terms of CV, increasing by approximately 1.83, 1.18, 1.75, and 1.72-fold, respectively. Through a comprehensive evaluation of the simulation and clinical study results, it was demonstrated that the BM3D algorithm with the optimized \(\sigma\)-value had superior performance compared to that of the conventional noise reduction algorithms used in this study. However, our results were conducted by applying a commonly available \(\sigma\)-value at different noise levels through simulation studies. Thus, the optimized \(\sigma\)-value may not show \"perfect\" performance under all equipment and shooting conditions. Additionally, MRI requires an expeditious image-processing technique. In this study, the time required for image processing using the BM3D algorithm was measured as follows: first, in optimizing the BM3D algorithm using simulated brain T2 Wis, it took approximately 0.11 sec per image for a matrix size of 217 \(\times\) 181. In comparison, for clinical MR images with a matrix size of 256 \(\times\) 256, it took approximately 0.86 s.  
The BM3D algorithm has a relatively fast processing speed, but they actually have a considerable amount of processing time compared to that of conventional noise reduction algorithms because the BM3D algorithm does not perform image processing by simple calculations. This process involves converting 2D patches into 3D blocks; the signal in the spatial domain is converted to the frequency domain, and noise reduction is performed twice through hard thresholding and Wiener filtering. The proposed model used in this study achieved significant noise reduction performance compared to conventional noise reduction algorithms based on quantitative evaluation. However, improvement is necessary to shorten the time required for using the BM3D algorithm. Therefore, we plan to compensate for the processing time by adopting machine learning techniques that can simplify the image processing step while preserving the noise reduction performance along with the optimization of the BM3D algorithm in further study. Brain MR images and numerous cognitive ability indicators are used to diagnose Alzheimer's disease (AD) [37; 38]. In particular, the expansion of the ventricles, which is considered important for visually evaluating the progress of AD, can be observed in brain MR images. No prominent difference was found between conventional noise reduction algorithms in clinical studies, while the quantitative image quality of the optimized BM3D algorithm was observed to be the most superior among all. In future studies, to secure reliability for versatility, we plan on applying the BM3D algorithm with optimized \(\sigma\)-values to clinical MR images acquired using various pulse sequences, such as echo planar imaging, to evaluate the algorithm's performance across different sequences and establish its effectiveness in noise reduction and image quality improvement in diverse clinical scenarios.