Image Super-Resolution via Hierarchical and Collaborative Sparse Representation

In this paper, we propose an efficient image super-resolution algorithm based on hierarchical and collaborative sparse representation (HCSR). Motivated by the observation that natural images typically exhibit multi-modal statistics, we propose a hierarchical sparse coding model which includes two layers: the first layer encodes individual patches, and the second layer jointly encodes the set of patches that belong to the same homogeneous subset of image space. We further present a simple alternative to achieve such target by identifying optimal sparse representation that is adaptive to specific statistics of images. Specially, we cluster images from the offline training set into regions of similar geometric structure, and model each region (cluster) by learning adaptive bases describing the patches within that cluster using principal component analysis (PCA). This cluster-specific dictionary is then exploited to optimally estimate the underlying HR pixel values using the idea of collaborative sparse coding, in which the similarity between patches in the same cluster is further considered. It conceptually and computationally remedies the limitation of many existing algorithms based on standard sparse coding, in which patches are independently encoded. Experimental results demonstrate the proposed method appears to be competitive with state-of-the-art algorithms.