Perturbation of the eigenvectors of the graph Laplacian: Application to image denoising

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] and [2], and theoretical analyses of patch denoising algorithms (Levin et al., 2012) [3], (Taylor and Meyer, 2012) [4].