Seven ways to improve example-based single image super resolution

In this paper we present seven techniques that everybody should know to improve example-based single image super resolution (SR): 1) augmentation of data, 2) use of large dictionaries with efficient search structures, 3) cascading, 4) image self-similarities, 5) back projection refinement, 6) enhanced prediction by consistency check, and 7) context reasoning. We validate our seven techniques on standard SR benchmarks (i.e. Set5, Set14, B100) and methods (i.e. A+, SRCNN, ANR, Zeyde, Yang) and achieve substantial improvements.The techniques are widely applicable and require no changes or only minor adjustments of the SR methods. Moreover, our Improved A+ (IA) method sets new state-of-the-art results outperforming A+ by up to 0.9dB on average PSNR whilst maintaining a low time complexity.Comment: 9 page

Structured Sparsity: Discrete and Convex approaches

Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics applications: While the ambient dimension is vast in modern data analysis problems, the relevant information therein typically resides in a much lower dimensional space. However, many solutions proposed nowadays do not leverage the true underlying structure. Recent results in CS extend the simple sparsity idea to more sophisticated {\em structured} sparsity models, which describe the interdependency between the nonzero components of a signal, allowing to increase the interpretability of the results and lead to better recovery performance. In order to better understand the impact of structured sparsity, in this chapter we analyze the connections between the discrete models and their convex relaxations, highlighting their relative advantages. We start with the general group sparse model and then elaborate on two important special cases: the dispersive and the hierarchical models. For each, we present the models in their discrete nature, discuss how to solve the ensuing discrete problems and then describe convex relaxations. We also consider more general structures as defined by set functions and present their convex proxies. Further, we discuss efficient optimization solutions for structured sparsity problems and illustrate structured sparsity in action via three applications.Comment: 30 pages, 18 figure