Learning Quaternion Graph for Color Face Image Super-Resolution

Most of the existing face image super-resolution methods are designed for grayscale images. For color images, these methods just treat each color channel individually or considered the illumination part only, ignoring the relationships among different color channels. To address this concern, in this paper we present a color face image super-resolution method by learning the quaternion graph (LQG) representation. Instead of spatial domain, the color image is represented in the quaternionic domain, which encourages the proposed model to well preserve the correlations among different color channels. Besides, a graph regularization is learned in the quaternion space to ensure the smoothness of encoding feature space. More specifically, by utilizing the graph Laplacian, we present to promote the smoothness of representations by forcing similar training samples to share similar encoding coefficients. This not only helps to stabilize the linear system but also makes the model more robust to noise. Experimental results demonstrated the efficiency of the proposed method in super-resolving color face images.