Spectral design of signaladapted tight frames on graphs
(2019) In Signals and Communication Technology p.177206 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 coarsetofine 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
 18604870
 18604862
 ISBN
 9783030035730
 9783030035747
 DOI
 10.1007/9783030035747_4
 language
 English
 LU publication?
 yes
 id
 1205047447c644aa91fcbbc8de3d9158
 date added to LUP
 20190405 15:12:59
 date last changed
 20190423 04:48:52
@inbook{1205047447c644aa91fcbbc8de3d9158, 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 coarsetofine representations.</p>}, author = {Behjat, Hamid and Van De Ville, Dimitri}, isbn = {9783030035730}, issn = {18604870}, language = {eng}, pages = {177206}, publisher = {Springer}, series = {Signals and Communication Technology}, title = {Spectral design of signaladapted tight frames on graphs}, url = {http://dx.doi.org/10.1007/9783030035747_4}, year = {2019}, }