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

被引：0
作者：
Lu Yu
Jun Xie
Xiang Zheng
机构：
[1] Army Engineering University of PLA,Institute of Communications Engineering
[2] Army Engineering University of PLA,College of Command and Control Engineering
来源：
Signal, Image and Video Processing | 2023年 / 17卷
关键词：
Graph Fourier transform; Discrete cosine transform; Laplacian matrix;
D O I：
暂无
中图分类号：
学科分类号：
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
收藏
页码：445 / 451
页数：6
相关论文
共 51 条
  • [1] Gupta V(2021)ECG signal analysis using CWT, spectrogram and autoregressive technique Iran J. Comput. Sci. 6 260-285
  • [2] Mittal M(2019)A comparison of ECG signal pre-processing using FrFT, FrWT and IPCA for improved analysis Innov. Res. Biomed. En 40 145-156
  • [3] Mittal V(2016)Graph signal denoising via trilateral filter on graph spectral domain IEEE Trans. Signal Inf. Process. Over Netw. 2 137-148
  • [4] Gupta V(2021)Adaptive graph filtering with intra-patch pixel smoothing for image denoising Circuits Syst. Signal Process. 40 5381-5400
  • [5] Mittal M(2020)A robust 3D point cloud watermarking method based on the graph Fourier transform Multimed. Tools Appl. 79 1921-1950
  • [6] Onuki M(2022)Generic reversible visible watermarking via regularized graph Fourier transform coding IEEE Trans. Image Process. 31 691-705
  • [7] Ono S(2021)Graph Fourier transform based audio zero-watermarking IEEE Signal Process. Lett. 28 1943-1947
  • [8] Yamagishi M(2020)Compressive sensing of multichannel EEG signals based on graph Fourier transform and cosparsity Neural Process. Lett. 51 1227-1236
  • [9] Tang Y(2021)Mining graph-Fourier transform time series for anomaly detection of internet traffic at core and metro networks IEEE Access 9 8997-9011
  • [10] Sun J(2020)Fast incremental spectral clustering in titanate application via graph Fourier transform IEEE Access 8 57,252-57,259
123456