Graph-Based Manifold Frequency Analysis for Denoising
This addresses denoising for manifold data, which is incremental as it adapts wavelet-based methods to graph domains.
The paper tackles the problem of denoising data on manifolds by proposing a graph-based frequency analysis framework, achieving significant performance improvements over state-of-the-art methods with robustness to parameter variations.
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.