Sparse representation for image super-resolution

Abstract

This chapter concentrates the problem of recovery a high-resolution (HR) image from a single low-resolution input image. Recent research proposed to deal with the image super-resolution problem with sparse coding, which is based on the well reconstruction of any local image patch by a sparse linear combination of an appropriately chosen over-complete dictionary. Therein the chosen LR (Low-resolution) and HR (High-resolution) dictionaries have to be exactly corresponding for well reconstructing the local image patterns. However, the conventional sparse coding based image super-resolution usually achieves a global dictionary D=[D l ; D h ] by jointly training the concatenated LR and HR local image patches, and then reconstruct the LR and HR image as a linear combination of the separated D l and D h . This strategy only can achieve the global minimum reconstructing error of LR and HR local patches, and usually cannot obtain the exactly corresponding LR and HR dictionaries. In addition, the accurate coefficients for reconstructing the HR image patch using HR dictionary D h are also unable to be estimated using only the LR input and the LR dictionary D l . Therefore, this paper proposes to firstly learn the HR dictionary D h from the features of the training HR local patches, and then propagates the HR dictionary to the LR one, called as HR2LR dictionary propagation, by mathematical proving and statistical analysis. The effectiveness of the proposed HR2LR dictionary propagation in sparse coding for super-resolution is demonstrated by comparison with the conventional super-resolution approaches such as sparse coding and interpolation. © 2014 Springer-Verlag Berlin Heidelberg.