## 5 Conclusions  
In this study, we aimed to optimize the \(\sigma\)-value of the BM3D algorithm to achieve efficient noise reduction. For this purpose, we obtained brain T2 WIs acquired using the BrainWeb simulation program and clinical MR images from the ADNI dataset. Rician noise with intensities of 0.05, 0.10, and 0.15 was added to these images, and the \(\sigma\)-values of the BM3D algorithm were incrementally increased from 0.01 to 0.99 with a step size of 0.01. Furthermore, in the simulation study of the optimized BM3D algorithm, we observed that sigma values of 0.08, 0.13, and 0.15 demonstrated the most improved image characteristics for each noise level. The optimal \(\sigma\)-value was derived from the average of these values. Additionally, to verify its performance on actual clinical images, we applied the optimized BM3D algorithm to brain T2 WIs obtained from the ADNI dataset. The results demonstrated a trend similar to the simulation findings, and the optimized BM3D algorithm exhibited superior similarity to the conventional noise reduction algorithms. In conclusion, applying the BM3D algorithm with a \(\sigma\)-value of 0.12 to brain T2 WIs can provide excellent noise reduction effects, despite the relatively longer processing time compared to that of conventional noise reduction algorithms. The purpose of medical image processing is to acquire clear medical images with noise excluded, enabling accurate and rapid diagnosis. The results of this study demonstrate that the optimized sigma value derived from the BM3D algorithm effectively suppresses excessive smoothing, allowing for efficient noise reduction. It is inferred that this approach can be effectively applied in practical clinical settings. Conceptualization, M.P. and Y.L. ; Methodology, S.-H.K. and K.K. ; Software, M.P. and S.-H.K. ; Validation, Y.L. ; Formal analysis, M.P. and Y.L. ; Investigation, M.P., S.-H.K., K.K. and Y.L. ; Data curation, M.P. and K.K. ; Writing--original draft preparation, M.P. and S.-H.K. ; Writing--review and editing, K.K. and Y.L. ; Project administration, Y.L. All authors have read and agreed to the published version of the manuscript. This research received no funding. The study was conducted according to the guidelines of the Declaration of Helsinki and approved by the Institutional Review Board of Gachon University (1044396-202303-HR-031-01). A benchmark dataset, the Alzheimer's Disease Neuroimaging Initiative (ADNI), which was used in our work, obtained informed consent from the participants. More information can be found in the following link: \"[[http://adni.loni.usc.edu/study-design/](http://adni.loni.usc.edu/study-design/)]([http://adni.loni.usc.edu/study-design/](http://adni.loni.usc.edu/study-design/))(accessed on 29 June 2023)\". Data availability Statement: Data used in the preparation of this article were obtained from the ADNI database (adni.loni.usc.edu). The ADNI was launched in 2003 as a public-private partnership led by Principal Investigator [PERSON], MD. The primary goal of the ADNI has been to test whether serial magnetic resonance imaging (MRI), positron emission tomography (PET), other biological markers, and clinical and neuropsychological assessments can be combined to measure the progression of mild cognitive impairment (MCI) and early Alzheimer's disease (AD). For up-to-date information, see www.adni.loni.info.org. Data collection and sharing for this project was funded by the Alzheimer's Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense award number W81 XWH-12-2-0012).