  Image interpolation is a special case of image super-resolution, where the
low-resolution image is directly down-sampled from its high-resolution
counterpart without blurring and noise. Therefore, assumptions adopted in
super-resolution models are not valid for image interpolation. To address this
problem, we propose a novel image interpolation model based on sparse
representation. Two widely used priors including sparsity and nonlocal
self-similarity are used as the regularization terms to enhance the stability
of interpolation model. Meanwhile, we incorporate the nonlocal linear
regression into this model since nonlocal similar patches could provide a
better approximation to a given patch. Moreover, we propose a new approach to
learn adaptive sub-dictionary online instead of clustering. For each patch,
similar patches are grouped to learn adaptive sub-dictionary, generating a more
sparse and accurate representation. Finally, the weighted encoding is
introduced to suppress tailing of fitting residuals in data fidelity. Abundant
experimental results demonstrate that our proposed method outperforms several
state-of-the-art methods in terms of quantitative measures and visual quality.
