Position constraint based face image super-resolution by learning multiple local linear projections

•We propose to train multiple local linear projections under the position constraint.•Patches of the same position are assumed to favor the same local mapping function.•Sparse inner structure of LR patches is expected to be preserved by the HR ones.•HR patch is directly generated using the corresponding local linear projection.•State-of-the-art visual and quantitative results have been achieved.

In recent years, many super-resolution methods reveal that the mapping between low- and high-resolution images can be approximated by multiple local linear ones. Moreover, since face image patches located at the same position resemble each other, it is reasonable to assume they favor the same local linear mapping. Inspired by these phenomena, we propose a position constraint based face image super-resolution method which offline trains multiple local linear projections. Two goals are incorporated: First, a low-resolution patch can be linearly mapped to a high-resolution patch using the corresponding local linear projection. Second, the intrinsic sparse structure between low-resolution patches should be preserved by the reconstructed high-resolution ones. The final high-resolution face image is formed by integrating the reconstructed patches. Experimental results demonstrate that the proposed method can achieve face images of satisfactory quality and the online reconstruction stage is computationally fast. Besides, to some extent, the proposed method is insensitive to overlap size and the number of training images.