000190280 001__ 190280
000190280 005__ 20190416055537.0
000190280 0247_ $$2doi$$a10.1109/Tsp.2015.2424203
000190280 022__ $$a1053-587X
000190280 02470 $$2ISI$$a000357778600006
000190280 037__ $$aARTICLE
000190280 245__ $$aSpectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Frames
000190280 269__ $$a2015
000190280 260__ $$bInstitute of Electrical and Electronics Engineers$$c2015
000190280 336__ $$aJournal Articles
000190280 520__ $$aWe consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph wavelet constructions are only adapted to the length of the spectrum, the filters proposed in this paper are adapted to the distribution of graph Laplacian eigenvalues, and therefore lead to atoms with better discriminatory power. Our approach is to first characterize a family of systems of uniformly translated kernels in the graph spectral domain that give rise to tight frames of atoms generated via generalized translation on the graph. We then warp the uniform translates with a function that approximates the cumulative spectral density function of the graph Laplacian eigenvalues. We use this approach to construct computationally efficient, spectrum-adapted, tight vertex-frequency and graph wavelet frames. We give numerous examples of the resulting spectrum-adapted graph filters, and also present an illustrative example of vertex-frequency analysis using the proposed construction.
000190280 6531_ $$aFilter design
000190280 6531_ $$asignal processing on graphs
000190280 6531_ $$aspectrum-based warping
000190280 6531_ $$atight frames
000190280 6531_ $$avertex-frequency analysis
000190280 700__ $$0242930$$g201233$$aShuman, David
000190280 700__ $$aWiesmeyr, Christoph
000190280 700__ $$aHolighaus, Nicki
000190280 700__ $$0240428$$g120906$$aVandergheynst, Pierre
000190280 773__ $$j63$$tIEEE Transactions on Signal Processing$$k16$$q4223-4235
000190280 8564_ $$uhttps://infoscience.epfl.ch/record/190280/files/Shuman_et_al_Spectrum_Adapted_Frames_2013.PDF$$zPreprint$$s3119273$$yPreprint
000190280 909C0 $$xU10851$$0252393$$pLTS4
000190280 909C0 $$pLTS2$$xU10380$$0252392
000190280 909CO $$qGLOBAL_SET$$pSTI$$particle$$ooai:infoscience.tind.io:190280
000190280 917Z8 $$x201233
000190280 917Z8 $$x120906
000190280 917Z8 $$x120906
000190280 917Z8 $$x148230
000190280 937__ $$aEPFL-ARTICLE-190280
000190280 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000190280 980__ $$aARTICLE