Perturbation of the eigenvectors of the graph Laplacian: Application to image denoising |
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Affiliation: | 1. Department of Electrical Engineering, University of Colorado at Boulder, Boulder, CO, United States;2. Department of Diagnostic Radiology, Yale University, CT, United States |
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Abstract: | Patch-based denoising algorithms currently provide the optimal techniques to restore an image. These algorithms denoise patches locally in “patch-space”. In contrast, we propose in this paper a simple method that uses the eigenvectors of the Laplacian of the patch-graph to denoise the image. Experiments demonstrate that our denoising algorithm outperforms the denoising gold-standards. We provide an analysis of the algorithm based on recent results on the perturbation of kernel matrices (El Karoui, 2010) [1], [2], and theoretical analyses of patch denoising algorithms (Levin et al., 2012) [3], (Taylor and Meyer, 2012) [4]. |
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Keywords: | Graph Laplacian Eigenvector perturbation Random kernel matrix Patch Image denoising |
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