Most face super-resolution methods assume that low- and high-resolution manifolds have similar local geometrical structure; hence, learn local models on the low-resolution manifold (e.g., sparse or locally linear embedding models), which are then applied on the high-resolution manifold. However, the low-resolution manifold is distorted by the one-to-many relationship between low- and high-resolution patches. This paper presents the Linear Model of Coupled Sparse Support (LM-CSS) method, which learns linear models based on the local geometrical structure on the high-resolution manifold rather than on the low-resolution manifold. For this, in a first step, the low-resolution patch is used to derive a globally optimal estimate of the high-resolution patch. The approximated solution is shown to be close in the Euclidean space to the ground truth, but is generally smooth and lacks the texture details needed by the state-of-the-art face recognizers. Unlike existing methods, the sparse support that best estimates the first approximated solution is found on the high-resolution manifold. The derived support is then used to extract the atoms from the coupled low- and high-resolution dictionaries that are most suitable to learn an up-scaling function for every facial region. The proposed solution was also extended to compute face super-resolution of non-frontal images. Extensive experimental results conducted on a total of 1830 facial images show that the proposed method outperforms seven face super-resolution and a state-of-the-art cross-resolution face recognition method in terms of both quality and recognition.
