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.
Original language | English |
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Title of host publication | 2021 29th European Signal Processing Conference (EUSIPCO) |
Subtitle of host publication | Proceedings |
Publisher | IEEE |
Pages | 2005-2009 |
Number of pages | 5 |
ISBN (Electronic) | 978-9-0827-9706-0 |
ISBN (Print) | 978-1-6654-0900-1 |
DOIs | |
Publication status | Published - 2021 |
Event | 2021 29th European Signal Processing Conference (EUSIPCO) - Virtual at Dublin, Ireland Duration: 23 Aug 2021 → 27 Aug 2021 Conference number: 29th |
Conference
Conference | 2021 29th European Signal Processing Conference (EUSIPCO) |
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Abbreviated title | EUSIPCO 2021 |
Country/Territory | Ireland |
City | Virtual at Dublin |
Period | 23/08/21 → 27/08/21 |
Bibliographical note
Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-careOtherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
Keywords
- Hodge decomposition
- Hodge Laplacian
- simplicial complexes
- simplicial filters
- Topological signal processing