Perturbation of the Eigenvectors of the Graph Laplacian: Application to Image Denoising
This addresses image denoising for computer vision applications, but appears incremental as it builds on existing graph-based methods.
The paper tackled image denoising by analyzing how noise affects eigenvectors of the graph Laplacian for image patches, resulting in an algorithm that outperforms gold-standard denoising methods.
The original contributions of this paper are twofold: a new understanding of the influence of noise on the eigenvectors of the graph Laplacian of a set of image patches, and an algorithm to estimate a denoised set of patches from a noisy image. The algorithm relies on the following two observations: (1) the low-index eigenvectors of the diffusion, or graph Laplacian, operators are very robust to random perturbations of the weights and random changes in the connections of the patch-graph; and (2) patches extracted from smooth regions of the image are organized along smooth low-dimensional structures in the patch-set, and therefore can be reconstructed with few eigenvectors. Experiments demonstrate that our denoising algorithm outperforms the denoising gold-standards.