Abstract
This paper proposes convolutional filtering for data whose structure can be modeled by a simplicial complex (SC). SCs are mathematical tools that not only capture pairwise relationships as graphs but account also for higher-order network structures. These filters are built by following the shift-and-sum principle of the convolution operation and rely on the Hodge-Laplacians to shift the signal within the simplex. But since in SCs we have also inter-simplex coupling, we use the incidence matrices to transfer the signal in adjacent simplices and build a filter bank to jointly filter signals from different levels. We prove some interesting properties for the proposed filter bank, including permutation and orientation equivariance, a computational complexity that is linear in the SC dimension, and a spectral interpretation using the simplicial Fourier transform. We illustrate the proposed approach with numerical experiments.
Original language | English |
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Title of host publication | Proceedings of the ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) |
Place of Publication | Piscataway |
Publisher | IEEE |
Pages | 5578-5582 |
Number of pages | 5 |
ISBN (Electronic) | 978-1-6654-0540-9 |
ISBN (Print) | 978-1-6654-0541-6 |
DOIs | |
Publication status | Published - 2022 |
Event | ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) - Singapore, Singapore Duration: 23 May 2022 → 27 May 2022 |
Conference
Conference | ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) |
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Country/Territory | Singapore |
City | Singapore |
Period | 23/05/22 → 27/05/22 |
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 Laplacian
- simplicial filter
- topological signal processing