Are There Approximate Fast Fourier Transforms On Graphs?

Luc Le Magoarou 1 Rémi Gribonval 1
1 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : Signal processing on graphs is a recent research domain that seeks to extend classical signal processing tools such as the Fourier transform to irregular domains given by a graph. In such a graph setting, a way to rapidly apply the Fourier transform, i.e. a Fast Fourier Transform (FFT), is lacking. In this paper, we propose to leverage the recently introduced Flexible Approximate MUlti-layer Sparse Transforms (FAµST) in order to compute approximate FFTs on graphs. The approach is first described, then validated on several types of classical graphs and finally used for fast filtering, showing good potential .
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Luc Le Magoarou, Rémi Gribonval. Are There Approximate Fast Fourier Transforms On Graphs? . International Conference on Acoustics, Speech and Signal Processing (ICASSP), Mar 2016, Shanghai, China. ⟨hal-01254108v2⟩

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