Spectral design of signal-adapted tight frames on graphs
(2019) In Signals and Communication Technology p.177-206- Abstract
Analysis of signals defined on complex topologies modeled by graphs is a topic of increasing interest. Signal decomposition plays a crucial role in the representation and processing of such information, in particular, to process graph signals based on notions of scale (e.g., coarse to fine). The graph spectrum is more irregular than for conventional domains; i.e., it is influenced by graph topology, and, therefore, assumptions about spectral representations of graph signals are not easy to make. Here, we propose a tight frame design that is adapted to the graph Laplacian spectral content of a given class of graph signals. The design exploits the ensemble energy spectral density, a notion of spectral content of the given signal set that... (More)
Analysis of signals defined on complex topologies modeled by graphs is a topic of increasing interest. Signal decomposition plays a crucial role in the representation and processing of such information, in particular, to process graph signals based on notions of scale (e.g., coarse to fine). The graph spectrum is more irregular than for conventional domains; i.e., it is influenced by graph topology, and, therefore, assumptions about spectral representations of graph signals are not easy to make. Here, we propose a tight frame design that is adapted to the graph Laplacian spectral content of a given class of graph signals. The design exploits the ensemble energy spectral density, a notion of spectral content of the given signal set that we determine either directly using the graph Fourier transform or indirectly through approximation using a decomposition scheme. The approximation scheme has the benefit that (i) it does not require diagonalization of the Laplacian matrix, and (ii) it leads to a smooth estimate of the spectral content. A prototype system of spectral kernels each capturing an equal amount of energy is defined. The prototype design is then warped using the signal set’s ensemble energy spectral density such that the resulting subbands each capture an equal amount of ensemble energy. This approach accounts at the same time for graph topology and signal features, and it provides a meaningful interpretation of subbands in terms of coarse-to-fine representations.
(Less)
- author
- Behjat, Hamid LU and Van De Ville, Dimitri
- organization
- publishing date
- 2019
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Signals and Communication Technology
- series title
- Signals and Communication Technology
- pages
- 30 pages
- publisher
- Springer
- external identifiers
-
- scopus:85063228248
- ISSN
- 1860-4870
- 1860-4862
- ISBN
- 978-3-030-03574-7
- 978-3-030-03573-0
- DOI
- 10.1007/978-3-030-03574-7_4
- language
- English
- LU publication?
- yes
- id
- 12050474-47c6-44aa-91fc-bbc8de3d9158
- date added to LUP
- 2019-04-05 15:12:59
- date last changed
- 2024-03-19 03:51:12
@inbook{12050474-47c6-44aa-91fc-bbc8de3d9158,
abstract = {{<p>Analysis of signals defined on complex topologies modeled by graphs is a topic of increasing interest. Signal decomposition plays a crucial role in the representation and processing of such information, in particular, to process graph signals based on notions of scale (e.g., coarse to fine). The graph spectrum is more irregular than for conventional domains; i.e., it is influenced by graph topology, and, therefore, assumptions about spectral representations of graph signals are not easy to make. Here, we propose a tight frame design that is adapted to the graph Laplacian spectral content of a given class of graph signals. The design exploits the ensemble energy spectral density, a notion of spectral content of the given signal set that we determine either directly using the graph Fourier transform or indirectly through approximation using a decomposition scheme. The approximation scheme has the benefit that (i) it does not require diagonalization of the Laplacian matrix, and (ii) it leads to a smooth estimate of the spectral content. A prototype system of spectral kernels each capturing an equal amount of energy is defined. The prototype design is then warped using the signal set’s ensemble energy spectral density such that the resulting subbands each capture an equal amount of ensemble energy. This approach accounts at the same time for graph topology and signal features, and it provides a meaningful interpretation of subbands in terms of coarse-to-fine representations.</p>}},
author = {{Behjat, Hamid and Van De Ville, Dimitri}},
booktitle = {{Signals and Communication Technology}},
isbn = {{978-3-030-03574-7}},
issn = {{1860-4870}},
language = {{eng}},
pages = {{177--206}},
publisher = {{Springer}},
series = {{Signals and Communication Technology}},
title = {{Spectral design of signal-adapted tight frames on graphs}},
url = {{http://dx.doi.org/10.1007/978-3-030-03574-7_4}},
doi = {{10.1007/978-3-030-03574-7_4}},
year = {{2019}},
}