Multi-dimensional Graph Linear Canonical Transform
<|reference_start|>Multi-dimensional Graph Linear Canonical Transform: 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.<|reference_end|>
@article{li2024multi-dimensional,
    title={Multi-dimensional Graph Linear Canonical Transform},
    author={Na Li, Zhichao Zhang, Jie Han, Yunjie Chen, Chunzheng Cao},
    journal={arXiv preprint arXiv:2407.18931},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.18931},
    primaryClass={cs.IT eess.SP math.IT}
}