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

被引：4

作者：

Yu, Lu ^{[1
]}

Xie, Jun ^{[2
]}

Zheng, Xiang ^{[1
]}

机构：

[1] Army Engn Univ PLA, Inst Commun Engn, Houbiaoying Rd, Nanjing 210007, Peoples R China

[2] Army Engn Univ PLA, Coll Command & Control Engn, Houbiaoying Rd, Nanjing 210007, Jiangsu, Peoples R China

来源：

SIGNAL IMAGE AND VIDEO PROCESSING | 2023年 / 17卷 / 02期

关键词：

Graph Fourier transform; Discrete cosine transform; Laplacian matrix;

D O I：

10.1007/s11760-022-02249-5

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

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.

引用

页码：445 / 451

页数：7

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