Speckle noise in ultrasound imaging poses significant challenges by degrading image quality and affecting diagnostic precision. This study evaluates and compares the performance of established despeckling algorithms, including Lee, Kuan, Frost, Non-Local Means, and PMAD filters, as well as advanced techniques such as Fourth-Order Partial Differential Equations (PDEs) and a novel hybrid method combining Sticks filters with Fourth-Order PDE. Quantitative assessment was performed using metrics such as Peak Signal-to-Noise Ratio (PSNR), Mean Squared Error (MSE), Equivalent Number of Looks (ENL), Structural Similarity Index (SSI), Signal-to-Mean Power Index (SMPI), and computational efficiency. Among the evaluated methods, the Lee filter achieved the highest PSNR of 25.05 dB, demonstrating effective noise suppression while preserving the details of the image. The combination of Sticks and Fourth-Order PDE achieved the highest ENL of 0.0331, indicating superior smoothing in homogeneous regions and enhanced contrast. While PMAD exhibited superior speckle suppression with a minimal MSE of 886.49, it introduced slight blurring, compromising structural details. Visual inspections revealed that the hybrid Sticks and Fourth-Order PDE approach delivered exceptional edge preservation and contrast enhancement, outperforming other filters in clinical scenarios such as thyroid nodule analysis. The results demonstrate that the proposed hybrid method addresses critical trade-offs between noise suppression and detail preservation, offering a robust framework to improve the diagnostic utility of ultrasound images. Future research could explore optimizing these algorithms for real-time applications, enabling broader clinical adoption.