Medical Imaging: Denoising with Discrete Fourier Transform, Clustering, and Statistical Analysis

In the complex realm of medical imaging, noise poses a significant challenge as every pixel can convey crucial information that might save lives. Various factors, including environmental noise, sensor noise, and the intrinsic constraints of imaging equipment, can cause denoising in images. This study introduces a novel image denoising approach specifically applied to the Alzheimer's dataset, which is crucial for understanding and diagnosing Alzheimer's disease. The dataset comprises five distinct classes, each representing different stages or types of the disease, making it particularly significant in the medical field. Theproposed method leverages a combination of Discrete Fourier Transform (DFT), Inverse Discrete Fourier Transform (IDFT), Butterworth low-pass filtering, and Non-local Means denoising to enhance image quality. By employing Fourier Transform, the study performs frequency domain analysis on the image data, enabling the extraction of vital information while reducing noise. Furthermore, K-means clustering is used to categorize noisy and denoised images based on visual similarities. To validate the effectiveness of the denoising technique, statistical evaluations are conducted through hypothesis testing, comparing noise levelsand quality metrics between noisy and denoised images. Thisstudy not only offers a comprehensive approach to addressing the challenges of image denoising in medical imaging but alsohas significant societal benefits. By improving the clarity of images used in Alzheimer's research, the study contributes to more accurate diagnoses and better understanding of the disease, potentially leading to improved patient outcomes and advancing public health efforts in combating Alzheimer's disease.