  Manifold models consider natural-image patches to be on a low-dimensional
manifold embedded in a high dimensional state space and each patch and its
similar patches to approximately lie on a linear affine subspace. Manifold
models are closely related to semi-local similarity, a well-known property of
natural images, referring to that for most natural-image patches, several
similar patches can be found in its spatial neighborhood. Many approaches to
single image interpolation use manifold models to exploit semi-local similarity
by two mutually exclusive parts: i) searching each target patch's similar
patches and ii) operating on the searched similar patches, the target patch and
the measured input pixels to estimate the target patch. Unfortunately, aliasing
in the input image makes it challenging for both parts. A very few works
explicitly deal with those challenges and only ad-hoc solutions are proposed.
  To overcome the challenge in the first part, we propose a carefully-designed
adaptive technique to remove aliasing in severely aliased regions, which cannot
be removed from traditional techniques. This technique enables reliable
identification of similar patches even in the presence of strong aliasing. To
overcome the challenge in the second part, we propose to use the
aliasing-removed image to guide the initialization of the interpolated image
and develop a progressive scheme to refine the interpolated image based on
manifold models. Experimental results demonstrate that our approach
reconstructs edges with both smoothness along contours and sharpness across
profiles, and achieves an average Peak Signal-to-Noise Ratio (PSNR)
significantly higher than existing model-based approaches.
