Super resolution (SR) reconstruction is the process of fusing a sequence of low-resolution images into one high-resolution image. Many researchers have introduced various SR reconstruction methods. However, these traditional methods are limited in the extent to which they allow recovery of high-frequency information. Moreover, due to the self-similarity of face images, most of the facial SR algorithms are machine learning based. In this paper, we introduce a facial SR algorithm that combines learning-based and regularized SR image reconstruction algorithms. Our conception involves two main ideas. First, we employ separated frequency components to reconstruct high-resolution images. In addition, we separate the region of the training face image. These approaches can help to recover high-frequency information. In our experiments, we demonstrate the effectiveness of these ideas.