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The relationship between graph Fourier transform (GFT) and discrete cosine transform (DCT) for 1D signal and 2D image

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Abstract

Graph Fourier transform (GFT) is an important theoretical tool in spectral analysis of graph signal. This paper focuses on Laplacian-based GFT on two special cases of graph data. The relationship between GFT and discrete cosine transform (DCT) is revealed and proved formally. For 1D signal, we prove that GFT is unique and is equivalent to DCT. For 2D image, GFT has more than one basis, one of which is the DCT basis. The work in this paper would help reduce the computational complexity of GFT in special cases and contribute to a deeper understanding of GFT.

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Authors and Affiliations

  1. Institute of Communications Engineering, Army Engineering University of PLA, Houbiaoying Road, Nanjing, 210007, Jiangsu, China

    Lu Yu & Xiang Zheng

  2. College of Command and Control Engineering, Army Engineering University of PLA, Houbiaoying Road, Nanjing, 210007, Jiangsu, China

    Jun Xie

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  1. Lu Yu
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  2. Jun Xie
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  3. Xiang Zheng
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Correspondence to Jun Xie.

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Yu, L., Xie, J. & Zheng, X. The relationship between graph Fourier transform (GFT) and discrete cosine transform (DCT) for 1D signal and 2D image. SIViP 17, 445–451 (2023). https://doi.org/10.1007/s11760-022-02249-5

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  • DOI: https://doi.org/10.1007/s11760-022-02249-5

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