Hallucinating Color Face Image by Learning Graph Representation in Quaternion Space

Recently, learning-based representation techniques have been well exploited for grayscale face image hallucination. For color images, the previous methods only handle the luminance component or each color channel individually, without considering the abundant correlations among different channels as well as the inherent geometrical structure of data manifold. In this article, we propose a learning-based model in quaternion space with graph representation for color face hallucination. Instead of the spatial domain, the color image is represented in the quaternion domain to preserve correlations among different color channels. Moreover, a quaternion graph is learned to smooth the quaternion feature space, which helps to not only stabilize the linear system but also enclose the inherent topology structure of quaternion patch manifold. Besides, considering that single low-resolution (LR) image patch can just provide limited informative information in representation, we propose to simultaneously encode the query smaller LR patch as well as a larger patch containing the surrounding pixels seated at the same position in the objective. The larger patch with rich patterns is used to compensate the lost information in the query LR patch, which further enhances the manifold consistency assumption between the LR and HR patch spaces. The experimental results demonstrated the efficiency of the proposed method in hallucinating color face images.