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Conference Papers Year : 2021

Spectral folding and two-channel filter-banks on arbitrary graphs

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Abstract

In the past decade, several multi-resolution representation theories for graph signals have been proposed. Bipartite filter-banks stand out as the most natural extension of time domain filter-banks, in part because perfect reconstruction, orthogonality and bi-orthogonality conditions in the graph spectral domain resemble those for traditional filter-banks. Therefore, many of the well known orthogonal and bi-orthogonal designs can be easily adapted for graph signals. A major limitation is that this framework can only be applied to the normalized Laplacian of bipartite graphs. In this paper we extend this theory to arbitrary graphs and positive semi-definite variation operators. Our approach is based on a different definition of the graph Fourier transform (GFT), where orthogonality is defined with the respect to the Q inner product. We construct GFTs satisfying a spectral folding property, which allows us to easily construct orthogonal and bi-orthogonal perfect reconstruction filter-banks. We illustrate signal representation and computational efficiency of our filter-banks on 3D point clouds with hundreds of thousands of points.
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Dates and versions

hal-02988283 , version 1 (04-11-2020)
hal-02988283 , version 2 (07-11-2022)

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Eduardo Pavez, Benjamin Girault, Antonio Ortega, Philip A Chou. Spectral folding and two-channel filter-banks on arbitrary graphs. 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Jun 2021, Toronto, Canada. ⟨10.1109/ICASSP39728.2021.9414066⟩. ⟨hal-02988283v2⟩
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