000195213 001__ 195213
000195213 005__ 20190617200716.0
000195213 0247_ $$2doi$$a10.1109/Tsp.2014.2332441
000195213 022__ $$a1053-587X
000195213 02470 $$2ISI$$a000340092600010
000195213 037__ $$aARTICLE
000195213 245__ $$aLearning Parametric Dictionaries for Signals on Graphs
000195213 269__ $$a2014
000195213 260__ $$bInstitute of Electrical and Electronics Engineers$$c2014$$aPiscataway
000195213 300__ $$a14
000195213 336__ $$aJournal Articles
000195213 520__ $$aIn sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties – the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent signals residing on weighted graphs, an additional design challenge is to incorporate the intrinsic geometric structure of the irregular data domain into the atoms of the dictionary. In this work, we propose a parametric dictionary learning algorithm to design data-adapted, structured dictionaries that sparsely represent graph signals. In particular, we model graph signals as combinations of overlapping local patterns. We impose the constraint that each dictionary is a concatenation of subdictionaries, with each subdictionary being a polynomial of the graph Laplacian matrix, representing a single pattern translated to different areas of the graph. The learning algorithm adapts the patterns to a training set of graph signals. Experimental results on both synthetic and real datasets demonstrate that the dictionaries learned by the proposed algorithm are competitive with and often better than unstructured dictionaries learned by state-of-the-art numerical learning algorithms in terms of sparse approximation of graph signals. In contrast to the unstructured dictionaries, however, the dictionaries learned by the proposed algorithm feature localized atoms and can be implemented in a computationally efficient manner in signal processing tasks such as compression, denoising, and classification.
000195213 6531_ $$aDictionary learning
000195213 6531_ $$agraph signal processing
000195213 6531_ $$agraph Laplacian
000195213 6531_ $$asparse approximation
000195213 700__ $$0244101$$g185309$$aThanou, Dorina
000195213 700__ $$0242930$$g201233$$aShuman, David
000195213 700__ $$aFrossard, Pascal$$g101475$$0241061
000195213 773__ $$j62$$tIEEE Transactions on Signal Processing$$k15$$q3849-3862
000195213 8564_ $$uhttp://arxiv.org/pdf/1401.0887.pdf$$zURL
000195213 8564_ $$uhttps://infoscience.epfl.ch/record/195213/files/06842705.pdf$$zn/a$$s3999965$$yn/a
000195213 909C0 $$xU10851$$0252393$$pLTS4
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000195213 917Z8 $$x185309
000195213 917Z8 $$x185309
000195213 917Z8 $$x101475
000195213 917Z8 $$x185309
000195213 917Z8 $$x185309
000195213 917Z8 $$x185309
000195213 917Z8 $$x185309
000195213 937__ $$aEPFL-ARTICLE-195213
000195213 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000195213 980__ $$aARTICLE