Perturbation of the Eigenvectors of the Graph Laplacian: Application to Image Denoising

2012/02/29 by Meyer, Francois G., Shen, Xilin · 2 citations
#62H35 #Computer Vision and Pattern Recognition (cs.CV) #Data Analysis #FOS: Computer and information sciences #FOS: Physical sciences #G.3 #Machine Learning (stat.ML) #Statistics and Probability (physics.data-an)

paper · doi:10.48550/arxiv.1202.6666

Abstract

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.

Cited by

• Robust Tangent Space Estimation via Laplacian Eigenvector Gradient Orthogonalization
• Euclidean Distance Deflation Under High-Dimensional Heteroskedastic Noise

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