TY - JOUR
T1 - The windowed two-dimensional graph fractional Fourier transform
AU - Gan, Yu Chen
AU - Chen, Jian Yi
AU - Li, Bing Zhao
N1 - Publisher Copyright:
© 2025
PY - 2025/7
Y1 - 2025/7
N2 - In the vibrant landscape of image and signal processing, the research on multi-dimensional graph signals has been making remarkable strides. However, despite the progress, the in-depth exploration and analysis of graph signals defined on two-dimensional (2-D) Cartesian product graphs still present certain gaps and challenges. This paper presents a comprehensive investigation into the generalization of the windowed graph fractional Fourier transform (WGFRFT) in the context of 2-D Cartesian product graphs. Firstly, the 2-D WGFRFT and its inverse transform are meticulously derived and defined, accompanied by the proposal of a fast algorithm. Subsequently, through an experiment, the advantages of the 2-D WGFRFT over the WGFRFT in processing two-dimensional graph signals are verified. Moreover, the effectiveness of the fast algorithm is rigorously validated through vertex-frequency analysis. And lastly, based on the 2-D WGFRFT, a novel filter learning method is put forward, and its potential in image classification is demonstrated.
AB - In the vibrant landscape of image and signal processing, the research on multi-dimensional graph signals has been making remarkable strides. However, despite the progress, the in-depth exploration and analysis of graph signals defined on two-dimensional (2-D) Cartesian product graphs still present certain gaps and challenges. This paper presents a comprehensive investigation into the generalization of the windowed graph fractional Fourier transform (WGFRFT) in the context of 2-D Cartesian product graphs. Firstly, the 2-D WGFRFT and its inverse transform are meticulously derived and defined, accompanied by the proposal of a fast algorithm. Subsequently, through an experiment, the advantages of the 2-D WGFRFT over the WGFRFT in processing two-dimensional graph signals are verified. Moreover, the effectiveness of the fast algorithm is rigorously validated through vertex-frequency analysis. And lastly, based on the 2-D WGFRFT, a novel filter learning method is put forward, and its potential in image classification is demonstrated.
KW - Cartesian product graphs
KW - Fractional Fourier transform
KW - Graph Fourier transform
KW - Graph signal processing
UR - http://www.scopus.com/inward/record.url?scp=105001148932&partnerID=8YFLogxK
U2 - 10.1016/j.dsp.2025.105191
DO - 10.1016/j.dsp.2025.105191
M3 - Article
AN - SCOPUS:105001148932
SN - 1051-2004
VL - 162
JO - Digital Signal Processing: A Review Journal
JF - Digital Signal Processing: A Review Journal
M1 - 105191
ER -