The distribution of image data points forms its geometrical structure. This structure characterizes the local variation, and provides valuable heuristics to the regularization of image restoration process. However, most of the existing approaches to sparse coding fail to consider this character of the image. In this paper, we address the deblurring problem of image restoration. We analyze the distribution of the input data points. Inspired by the theory of manifold learning algorithm, we build a k-NN graph to character the geometrical structure of the data, so the local manifold structure of the data can be explicitly taken into account. To enforce the invariance constraint, we introduce a patch-similarity based term into the cost function which penalizes the nonlocal invariance of the image. Experimental results have shown the effectiveness of the proposed scheme.
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