Manifold denoising based on spectral graph wavelets

Abstract

We propose a new framework for manifold denoising using the Spectral Graph Wavelet transform, which enables non-iterative denoising directly in the graph frequency domain, an approach inspired by conventional wavelet-based signal denoising methods. We theoretically justify our approach, based on the fact that for smooth manifolds the coordinate information tends to create energy in the low spectral graph wavelet coefficients, while the noise affects all frequency bands in a similar way. Experimental results show that our suggested manifold frequency denoising (MFD) approach significantly outperforms the state of the art manifold denosing methods, and is robust to a wide range of parameter selections, e.g., the choice of k nearest neighbor connectivity of the graph.