  Super-resolution is an important but difficult problem in image/video
processing. If a video sequence or some training set other than the given
low-resolution image is available, this kind of extra information can greatly
aid in the reconstruction of the high-resolution image. The problem is
substantially more difficult with only a single low-resolution image on hand.
The image reconstruction methods designed primarily for denoising is
insufficient for super-resolution problem in the sense that it tends to
oversmooth images with essentially no noise. We propose a new adaptive linear
interpolation method based on variational method and inspired by local linear
embedding (LLE). The experimental result shows that our method avoids the
problem of oversmoothing and preserves image structures well.
