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Sparse representation-based image super-resolution is a well-studied topic; however, a general sparse framework that can utilize both internal and external dependencies remains unexplored. In this paper, we propose a group-structured sparse representation approach to make full use of both internal and external dependencies to facilitate image super-resolution. External compensated correlated information is introduced by a two-stage retrieval and refinement. First, in the global stage, the content-based features are exploited to select correlated external images. Then, in the local stage, the patch similarity, measured by the combination of content and high-frequency patch features, is utilized to refine the selected external data. To better learn priors from the compensated external data based on the distribution of the internal data and further complement their advantages, nonlocal redundancy is incorporated into …