In surveillance, subjects are often out of camera range, leading to low-resolution, unrecognizable face images. Addressing this, we propose a deep learning approach for single face super-resolution (SR) that focuses on enhancing facial features by weakening non-primary information with a novel loss function (WNI-L). This function prioritizes facial clarity over background, improving recognition. Additionally, we introduce an activation function with a threshold (ReLU-T) to normalize brightness variations, crucial for SR. Our method, combining WNI-L and ReLU-T, outperforms existing SOTA methods.