  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.
