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Signal-Adapted Tight Frames on Graphs

Behjat, Hamid LU ; Richter, Ulrike LU ; Van De Ville, Dimitri and Sörnmo, Leif LU (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
organization
publishing date
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
pages
13 pages
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:84993907193
  • wos:000385378100020
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
2017-10-01 05:26:05
@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>},
  articleno    = {7513383},
  author       = {Behjat, Hamid and Richter, Ulrike and Van De Ville, Dimitri and Sörnmo, Leif},
  issn         = {1053-587X},
  keyword      = {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},
  volume       = {64},
  year         = {2016},
}