Finite Impulse Response Filters for Simplicial Complexes

Maosheng Yang, Elvin Isufi, Michael T. Schaub, Geert Leus

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

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 languageEnglish
Title of host publication2021 29th European Signal Processing Conference (EUSIPCO)
Subtitle of host publicationProceedings
PublisherIEEE
Pages2005-2009
Number of pages5
ISBN (Electronic)978-9-0827-9706-0
ISBN (Print)978-1-6654-0900-1
DOIs
Publication statusPublished - 2021
Event2021 29th European Signal Processing Conference (EUSIPCO) - Virtual at Dublin, Ireland
Duration: 23 Aug 202127 Aug 2021
Conference number: 29th

Conference

Conference2021 29th European Signal Processing Conference (EUSIPCO)
Abbreviated titleEUSIPCO 2021
Country/TerritoryIreland
CityVirtual at Dublin
Period23/08/2127/08/21

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-care

Otherwise 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

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