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- W4372294857 abstract "In this paper, we introduce the two-dimensional spectral graph wavelet transform (SGWT) of discrete functions defined on weighted Cartesian product graphs. The graphs we consider are undirected, non-planar, and can be cyclic with no multiple loops and no multiple edges. We build this transform with the help of spectral decomposition of $$N_1N_2 times N_1N_2$$ Laplacian matrix $$mathcal {L}$$ of the Cartesian product graph $$G=G_1square G_2$$ , where $$N_1N_2$$ is the number of vertices of the Cartesian product graph. We have established the inversion formula for SGWT for continuous scale parameters $$s_1$$ and $$s_2$$ . By sampling the scale parameters at discrete values, we obtain discrete SGWT coefficients at different scales and vertices. We have obtained the frame bounds of the frame formed by the set of scaling and wavelet coefficients. Further, we have proved the localization result which holds for both normalized and non-normalized form of Laplacian. Towards the end, we have given the implementation details of SGWT through an example to show how to calculate the graph wavelet coefficients." @default.
- W4372294857 created "2023-05-07" @default.
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- W4372294857 date "2023-05-05" @default.
- W4372294857 modified "2023-10-17" @default.
- W4372294857 title "Multi-dimensional spectral graph wavelet transform" @default.
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- W4372294857 doi "https://doi.org/10.1007/s11760-023-02557-4" @default.
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