Graph-Based Manifold Frequency Analysis for Denoising

TL;DR

This paper introduces a novel graph Fourier domain approach for manifold denoising using spectral graph wavelets, which effectively separates signal from noise and outperforms existing methods.

Contribution

It presents a non-iterative denoising framework based on spectral graph wavelet transforms, justified by theoretical analysis of frequency localization for smooth manifolds.

Findings

Significantly outperforms state-of-the-art denoising methods

Robust to various parameter choices such as k-nearest neighbors

Effective in preserving manifold structure during denoising

Abstract

We propose a new framework for manifold denoising based on processing in the graph Fourier frequency domain, derived from the spectral decomposition of the discrete graph Laplacian. Our approach uses the Spectral Graph Wavelet transform in order to per- form 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 energy is localized in the low spectral graph wavelet sub-bands, while the noise affects all frequency bands in a similar way. Experimental results show that our proposed manifold frequency denoising (MFD) approach significantly outperforms the state of the art denoising meth- ods, and is robust to a wide range of parameter selections, e.g., the choice of k nearest neighbor connectivity of the graph.