Speckle noise significantly degrades the quality of images in domain especially in Synthetic Aperture Radar (SAR) and medical imaging, complicating the detection of critical features such as terrain details or tumors. The task of suppressing the speckle noise from images, known as despeckling, has significant importance in the field of image processing. In this study, we propose an innovative algorithm using Elementary Cellular Automata (ECAs) to reduce speckle noise. The methodology involves dividing an image into patches and converting pixel intensities within each patch into binary states. Using ECA rules, pixel values are iteratively adjusted to reduce noise while preserving details. To assess the effectiveness of our approach, we compare its performance with that of traditional filters using parameters like Peak-Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), Edge Preservation Index (EPI), and Perceptual Index (PI). The results of our ECA-based model achieved a PSNR of 28.532, surpassing traditional methods by significant margins: 8.1% higher than the Lee Filter, 12.8% above the Median Filter, 22.9% better than Anisotropic Diffusion, and over 57% higher than the Wiener Filter. The performance highlights the capability of our model in noise reduction compared to conventional approaches, offering a promising solution for applications in SAR and medical imaging.