This paper presents a novel approach to face super-resolution that explicitly models the relationship between low-resolution and high-resolution images. Unlike many existing methods, the proposed approach does not require a large number of high-resolution and low-resolution image pairs for training, making it applicable in scenarios with limited training data. By utilizing a feed-forward regression model, the proposed method provides a more interpretable and transparent approach to face super-resolution, enhancing the explainability of the super-resolution process. In particular, by progressively exploiting the contextual information of local patch, the proposed feed-forward regression method can model the relationship between the low-resolution and high-resolution images within a large receptive field. This is somewhat similar to the idea of convolutional neural networks, but the proposed approach is completely interpretable. Experimental results demonstrate that the proposed method achieves good performance in generating high-resolution face images, outperforming several existing methods. Overall, the proposed method contributes to advancing the field of face super-resolution by introducing a more interpretable and transparent approach that can achieve good results with minimal training data.