Synthetic Aperture Radar (SAR) systems generate high-resolution, all-weather Earth observation imagery; however, coherent microwave backscattering inherently introduces multiplicative speckle noise, which severely degrades feature extraction and target recognition. Although numerous despeckling techniques exist, a systematic comparative analysis across traditional spatial, multi-scale transform, and filtering paradigms remains crucial. In this paper, we present a comprehensive study and empirical evaluation of SAR image despeckling algorithms, categorizing existing methods into spatial-domain filters, frequency and multi-scale transform approaches (specifically Wavelet and Curvelet transforms), and non-local filtering frameworks like BM3D. To rigorously evaluate these techniques, we implemented a complete step-by-step MATLAB simulation pipeline. The empirical framework incorporates multiplicative speckle noise generation in the logarithmic domain, performance evaluation on synthetic degraded images, and testing across real Sentinel-1 C-band SAR scenes covering diverse homogeneous water bodies and heterogeneous urban landscapes. Performance is quantitatively benchmarked using Mean Squared Error (MSE), Peak Signal-to-Noise Ratio (PSNR), Noise Variance (NV), and Equivalent Number of Looks (ENL), alongside qualitative visual inspection. Experimental results demonstrate that applying logarithmic mapping to transform multiplicative speckle into an additive model, combined with directional Curvelet thresholding, outperforms standard isotropic Wavelet transforms by preserving fine structural boundaries and edge sharpness while achieving superior noise suppression (yielding higher PSNR and ENL values). Finally, we summarize the practical advantages, operational limitations, and key trade-offs to guide the selection of optimal despeckling workflows in remote sensing applications.