Signal-Adapted Tight Frames on Graphs
(2016) In IEEE Transactions on Signal Processing 64(22). p.6017-6029- Abstract
The analysis of signals on complex topologies modeled by graphs is a topic of increasing importance. Decompositions play a crucial role in the representation and processing of such information. Here, we propose a new tight frame design that is adapted to a class of signals on a graph. The construction starts from a prototype Meyer-type system of kernels with uniform subbands. The ensemble energy spectral density is then defined for a given set of signals defined on the graph. The prototype design is then warped such that the resulting subbands capture the same amount of energy for the signal class. This approach accounts at the same time for graph topology and signal features. The proposed frames are constructed for three different... (More)
The analysis of signals on complex topologies modeled by graphs is a topic of increasing importance. Decompositions play a crucial role in the representation and processing of such information. Here, we propose a new tight frame design that is adapted to a class of signals on a graph. The construction starts from a prototype Meyer-type system of kernels with uniform subbands. The ensemble energy spectral density is then defined for a given set of signals defined on the graph. The prototype design is then warped such that the resulting subbands capture the same amount of energy for the signal class. This approach accounts at the same time for graph topology and signal features. The proposed frames are constructed for three different graph signal sets and are compared with non-signal-adapted frames. Vertex localization of a set of resulting atoms is studied. The frames are then used to decompose a set of real graph signals and are also used in a setting of signal denoising. The results illustrate the superiority of the designed signal-adapted frames, over frames blind to signal characteristics, in representing data and in denoising.
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- author
- Behjat, Hamid LU ; Richter, Ulrike LU ; Van De Ville, Dimitri and Sörnmo, Leif LU
- organization
- publishing date
- 2016-11-15
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- filter design, signal processing on graphs, Spectral graph theory, tight frames
- in
- IEEE Transactions on Signal Processing
- volume
- 64
- issue
- 22
- article number
- 7513383
- pages
- 13 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- wos:000385378100020
- scopus:84993907193
- ISSN
- 1053-587X
- DOI
- 10.1109/TSP.2016.2591513
- language
- English
- LU publication?
- yes
- id
- 4e317d24-e651-4aa8-b746-0d1dfa93f99e
- date added to LUP
- 2016-11-18 14:17:39
- date last changed
- 2024-02-19 10:58:39
@article{4e317d24-e651-4aa8-b746-0d1dfa93f99e,
abstract = {{<p>The analysis of signals on complex topologies modeled by graphs is a topic of increasing importance. Decompositions play a crucial role in the representation and processing of such information. Here, we propose a new tight frame design that is adapted to a class of signals on a graph. The construction starts from a prototype Meyer-type system of kernels with uniform subbands. The ensemble energy spectral density is then defined for a given set of signals defined on the graph. The prototype design is then warped such that the resulting subbands capture the same amount of energy for the signal class. This approach accounts at the same time for graph topology and signal features. The proposed frames are constructed for three different graph signal sets and are compared with non-signal-adapted frames. Vertex localization of a set of resulting atoms is studied. The frames are then used to decompose a set of real graph signals and are also used in a setting of signal denoising. The results illustrate the superiority of the designed signal-adapted frames, over frames blind to signal characteristics, in representing data and in denoising.</p>}},
author = {{Behjat, Hamid and Richter, Ulrike and Van De Ville, Dimitri and Sörnmo, Leif}},
issn = {{1053-587X}},
keywords = {{filter design; signal processing on graphs; Spectral graph theory; tight frames}},
language = {{eng}},
month = {{11}},
number = {{22}},
pages = {{6017--6029}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
series = {{IEEE Transactions on Signal Processing}},
title = {{Signal-Adapted Tight Frames on Graphs}},
url = {{http://dx.doi.org/10.1109/TSP.2016.2591513}},
doi = {{10.1109/TSP.2016.2591513}},
volume = {{64}},
year = {{2016}},
}