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This paper presents a new paradigm for signal reconstruction and superresolution, correlation kernel analysis (CKA), that is based on the selection of a sparse set of bases from a large dictionary of class-specific basis functions. The basis functions that we use are the correlation functions of the class of signals we are analyzing. To choose the appropriate features from this large dictionary, we use support vector machine (SVM) regression and compare this to traditional principal component analysis (PCA) for the task of signal reconstruction. The testbed we use in this paper is a set of images of pedestrians. Based on the results presented here, we conclude that, when used with a sparse representation technique, the correlation function is an effective kernel for image reconstruction.