Patch-based Image Interpolation: Algorithms and Applications

Motivated by recent advances in adaptive sparse representations and nonlocal image modeling, we propose a patch-based image interpolation algorithm under a set theoretic framework. Our algorithm alternates the projection onto two convex sets: one is given by the observation data and the other defined by a sparsity-based nonlocal prior similar to BM3D. In order to optimize the design of observation constraint set, we propose to address the issue of sampling pattern and model it by a spatial point process. A Monte-Carlo based algorithm is proposed to optimize the randomness of sampling patterns to better approximate homogeneous Poisson process. Extensive experimental results in image interpolation and coding applications are reported to demonstrate the potential of the proposed algorithms.