Most face super-resolution methods assume that low-resolution and high-resolution manifolds have similar local geometrical structure, hence learn local models on the lowresolution manifolds (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 oneto-many relationship between low- and high- resolution patches. This paper presents a 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 Euclidean space to the ground-truth but is generally smooth and lacks the texture details needed by state-ofthe-art face recognizers. This first estimate allows us to find the support of the high-resolution manifold using sparse coding (SC), which are then used as support for learning a local projection (or upscaling) model between the low-resolution and the highresolution manifolds using Multivariate Ridge Regression (MRR). Experimental results show that the proposed method outperforms six face super-resolution methods in terms of both recognition and quality. These results also reveal that the recognition and quality are significantly affected by the method used for stitching all super-resolved patches together, where quilting was found to better preserve the texture details which helps to achieve higher recognition rates.
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