Related papers: Finite Impulse Response Filters for Simplicial Complexes

Finite Impulse Response Filters for Simplicial Complexes

URL: http://arxiv.org/abs/2103.12587v1
Date: Tue, 23 Mar 2021 14:41:45 GMT
Title: Finite Impulse Response Filters for Simplicial Complexes
Authors: Maosheng Yang and Elvin Isufi and Michael T. Schaub and Geert Leus
Abstract summary: We propose a finite impulse response filter based on the Hodge Laplacian. We show how this filter can be designed to amplify or attenuate certain spectral components of simplicial signals. Numerical experiments are conducted to show the potential of simplicial filters for sub-component extraction, denoising and model approximation.
Score: 34.47138649437185
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: In this paper, we study linear filters to process signals defined on simplicial complexes, i.e., signals defined on nodes, edges, triangles, etc. of a simplicial complex, thereby generalizing filtering operations for graph signals. We propose a finite impulse response filter based on the Hodge Laplacian, and demonstrate how this filter can be designed to amplify or attenuate certain spectral components of simplicial signals. Specifically, we discuss how, unlike in the case of node signals, the Fourier transform in the context of edge signals can be understood in terms of two orthogonal subspaces corresponding to the gradient-flow signals and curl-flow signals arising from the Hodge decomposition. By assigning different filter coefficients to the associated terms of the Hodge Laplacian, we develop a subspace-varying filter which enables more nuanced control over these signal types. Numerical experiments are conducted to show the potential of simplicial filters for sub-component extraction, denoising and model approximation.

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