In recent years, the field of machine learning has experienced significant growth, with the emergence of various advanced technologies leveraging its principles. Among these, Support Vector Regression (SVR) has established itself as a widely recognized and robust regression technique. This article introduces a novel approach, Robust Hampel Weight-Based Support Vector Regression (RH-SVR), designed to enhance the resilience and efficiency of traditional SVR. The study investigates and compares several regression methods, including the Robust Linear Model (RLM), SVR, RH-SVR, and Least Squares Regression (LS). An experimental analysis was conducted using MRI images of the human heart and brain, both in their original form and with added noise at varying levels (10, 20, and 30%). Performance metrics such as Mean Square Error (MSE), Median Absolute Error (MDAE), Relative Standard Error (RSE), and Peak Signal-to-Noise Ratio (PSNR) were evaluated. The results consistently demonstrate that the proposed RH-SVR method achieves lower error rates and higher PSNR values, showcasing superior accuracy and robustness, particularly when processing noisy images.