  Face hallucination is a technique that reconstruct high-resolution (HR) faces
from low-resolution (LR) faces, by using the prior knowledge learned from HR/LR
face pairs. Most state-of-the-arts leverage position-patch prior knowledge of
human face to estimate the optimal representation coefficients for each image
patch. However, they focus only the position information and usually ignore the
context information of image patch. In addition, when they are confronted with
misalignment or the Small Sample Size (SSS) problem, the hallucination
performance is very poor. To this end, this study incorporates the contextual
information of image patch and proposes a powerful and efficient context-patch
based face hallucination approach, namely Thresholding Locality-constrained
Representation and Reproducing learning (TLcR-RL). Under the context-patch
based framework, we advance a thresholding based representation method to
enhance the reconstruction accuracy and reduce the computational complexity. To
further improve the performance of the proposed algorithm, we propose a
promotion strategy called reproducing learning. By adding the estimated HR face
to the training set, which can simulates the case that the HR version of the
input LR face is present in the training set, thus iteratively enhancing the
final hallucination result. Experiments demonstrate that the proposed TLcR-RL
method achieves a substantial increase in the hallucinated results, both
subjectively and objectively. Additionally, the proposed framework is more
robust to face misalignment and the SSS problem, and its hallucinated HR face
is still very good when the LR test face is from the real-world. The MATLAB
source code is available at https://github.com/junjun-jiang/TLcR-RL
