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arXiv · 2407.18931

Multi-dimensional Graph Linear Canonical Transform

Na Li·Zhichao Zhang·Jie Han·Yunjie Chen·Chunzheng Cao
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Abstract

Many multi-dimensional (M-D) graph signals appear in the real world, such as digital images, sensor network measurements and temperature records from weather observation stations. It is a key challenge to design a transform method for processing these graph M-D signals in the linear canonical transform domain. This paper proposes the two-dimensional graph linear canonical transform based on the central discrete dilated Hermite function (2-D CDDHFs-GLCT) and the two-dimensional graph linear canonical transform based on chirp multiplication-chirp convolution-chirp multiplication decomposition (2-D CM-CC-CM-GLCT). Then, extending 2-D CDDHFs-GLCT and 2-D CM-CC-CM-GLCT to M-D CDDHFs-GLCT and M-D CM-CC-CM-GLCT. In terms of the computational complexity, additivity and reversibility, M-D CDDHFs-GLCT and M-D CM-CC-CM-GLCT are compared. Theoretical analysis shows that the computational complexity of M-D CM-CC-CM-GLCT algorithm is obviously reduced. Simulation results indicate that M-D CM-CC-CM-GLCT achieves comparable additivity to M-D CDDHFs-GLCT, while M-D CM-CC-CM-GLCT exhibits better reversibility. Finally, M-D GLCT is applied to data compression to show its application advantages. The experimental results reflect the superiority of M-D GLCT in the algorithm design and implementation of data compression.

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Na Li, Zhichao Zhang, Jie Han, Yunjie Chen, Chunzheng Cao. 2024-07-10. Multi-dimensional Graph Linear Canonical Transform. https://arxiv.org/abs/2407.18931

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