Nonlinear neighbor embedding for single image super-resolution via kernel mapping

• We propose a nonlinear neighbor embedding method for single image super-resolution.
• The features are projected onto the high-dimensional spaces by nonlinear functions.
• The local structures of the LR and HR patch manifolds are assumed to be nonlinear.
• The kernel trick is utilized to solve the projection functions.
• The quality of final SR images is enhanced by scaling the high-frequency parts.

In this paper we propose a novel nonlinear neighbor embedding method for single image super-resolution (SR). Unlike previous works, the relationship between the local geometric structures of the two manifolds constructed by low-resolution (LR) and high-resolution (HR) patches are considered to be nonlinear in this paper. To achieve this goal, the original LR and HR patch features are mapped onto the underlying high-dimensional spaces respectively using two nonlinear mappings. Then the mapped features are projected by two jointly learnt linear matrices onto a unified feature subspace, where the conventional neighbor embedding is performed to reconstruct the target HR patches for the LR input. In addition, the kernel trick is applied to avoid the direct computation of nonlinear mapping functions, which facilitates the computation. The effectiveness of our approach is validated by experimental comparisons with several SR algorithms for the natural image super-resolution both quantitatively and qualitatively.