Signal-Adapted Tight Frames on Graphs

Behjat, HamidLund University,Lunds universitet,Avdelningen för Biomedicinsk teknik,Institutionen för biomedicinsk teknik,Institutioner vid LTH,Lunds Tekniska Högskola,Department of Biomedical Engineering,Departments at LTH,Faculty of Engineering, LTH (författare)

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.

Richter, UlrikeLund University,Lunds universitet,Integrativ neurofysiologi,Forskargrupper vid Lunds universitet,Integrative Neurophysiology,Lund University Research Groups(Swepub:lu)esx-urt (författare)
Van De Ville, DimitriSwiss Federal Institute of Technology (författare)
Sörnmo, LeifLund University,Lunds universitet,Avdelningen för Biomedicinsk teknik,Institutionen för biomedicinsk teknik,Institutioner vid LTH,Lunds Tekniska Högskola,Department of Biomedical Engineering,Departments at LTH,Faculty of Engineering, LTH(Swepub:lu)tde-lso (författare)
Avdelningen för Biomedicinsk teknikInstitutionen för biomedicinsk teknik (creator_code:org_t)

Av författaren/redakt...: Behjat, Hamid; Richter, Ulrike; Van De Ville, Di ...; Sörnmo, Leif

Om ämnet

TEKNIK OCH TEKNOLOGIER: TEKNIK OCH TEKNO ...; och Elektroteknik oc ...; och Signalbehandling

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