  In this paper, we propose a novel image interpolation algorithm, which is
formulated via combining both the local autoregressive (AR) model and the
nonlocal adaptive 3-D sparse model as regularized constraints under the
regularization framework. Estimating the high-resolution image by the local AR
regularization is different from these conventional AR models, which weighted
calculates the interpolation coefficients without considering the rough
structural similarity between the low-resolution (LR) and high-resolution (HR)
images. Then the nonlocal adaptive 3-D sparse model is formulated to regularize
the interpolated HR image, which provides a way to modify these pixels with the
problem of numerical stability caused by AR model. In addition, a new
Split-Bregman based iterative algorithm is developed to solve the above
optimization problem iteratively. Experiment results demonstrate that the
proposed algorithm achieves significant performance improvements over the
traditional algorithms in terms of both objective quality and visual perception
