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Design of graph filters and filterbanks

Nicolas Tremblay 1 Paulo Gonçalves 2 Pierre Borgnat 3
2 DANTE - Dynamic Networks : Temporal and Structural Capture Approach
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme, IXXI - Institut Rhône-Alpin des systèmes complexes
Abstract : Basic operations in graph signal processing consist in processing signals indexed on graphs either by filtering them or by changing their domain of representation, in order to better extract or analyze the important information they contain. The aim of this chapter is to review general concepts underlying such filters and representations of graph signals. We first recall the different Graph Fourier Transforms that have been developed in the literature, and show how to introduce a notion of frequency analysis for graph signals by looking at their variations. Then, we move to the introduction of graph filters, that are defined like the classical equivalent for 1D signals or 2D images, as linear systems which operate on each frequency of a signal. Some examples of filters and of their implementations are given. Finally, as alternate representations of graph signals, we focus on multiscale transforms that are defined from filters. Continuous multiscale transforms such as spectral wavelets on graphs are reviewed, as well as the versatile approaches of filterbanks on graphs. Several variants of graph filterbanks are discussed, for structured as well as arbitrary graphs, with a focus on the central point of the choice of the decimation or aggregation operators.
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Submitted on : Thursday, January 4, 2018 - 2:02:59 PM
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Nicolas Tremblay, Paulo Gonçalves, Pierre Borgnat. Design of graph filters and filterbanks. Petar M. Djurić; Cédric Richard. Cooperative and Graph Signal Processing, Academic Press, pp.299-324, 2018, 978-0-12-813677-5. ⟨10.1016/B978-0-12-813677-5.00011-0⟩. ⟨hal-01675375⟩



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