In the process of image acquisition, due to the limitation of imaging distance, imaging device resolution and other factors, it is difficult for the imaging devices to acquire all the significant information in the original scene without distortion, resulting in deformation, blur, down sampling results with noise. This paper proposes a resolution aiming at low-resolution and low prior knowledge of the human faces restoration. We take the image similarity based Expected Patch Log Likelihood (EPLL) framework to construct the distortion function of the face restoration effect, and use generative adversarial networks with completion function to restore the image. The proposed algorithm can maintain good contour and visual features of face images with 50% added noise and higher. Compared with traditional methods based on the image block similarity, this method can restore the 20% degraded image better. The statistical characteristics of the proposed algorithm have obvious advantages in PSNR and SSIM values in the experimental results.