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Recently, there has been a great deal of work developing super-resolution algorithms for combining a set of low-quality images to produce a set of higher quality images. Either explicitly or implicitly, such algorithms must perform the joint task of registering and fusing the low-quality image data. While many such algorithms have been proposed, very little work has addressed the performance bounds for such problems. In this paper, we analyze the performance limits from statistical first principles using Crame´r-Rao inequalities. Such analysis offers insight into the fundamental super-resolution performance bottlenecks as they relate to the subproblems of image registration, reconstruction, and image restoration.