  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.
