To super-resolve low-resolution (LR) face image suffering from strong noise and fuzzy interference, we present a novel approach for noisy face super-resolution (SR) that is based on three-level information representation constraints. To begin with, we develop a feature distillation network that focuses on extracting pertinent face information, which incorporates both statistical anti-interference models and latent contrast algorithms. Subsequently, we incorporate a face identity embedding model and a discrete wavelet transform model, which serve as additional supervision mechanisms for the reconstruction process. The face identity embedding model ensures the reconstruction of identity information in hypersphere identity metric space, while the discrete wavelet transform model operates in the wavelet domain to supervise the restoration of spatial structures. The experimental results clearly demonstrate the efficacy of our proposed method, which is evident through the lower Learned Perceptual Image Patch Similarity (LPIPS) score and Fréchet Inception Distances (FID), and overall practicability of the reconstructed images.