Multi-dimensional graph linear canonical transform and its application

Processing multi-dimensional (mD) graph data is crucial in fields such as social networks, communication networks, image processing, and signal processing due to its effective representation of complex relationships and network structures. Designing a transform method for processing these mD graph signals in the graph linear canonical domain remains a key challenge in graph signal processing. This article investigates new transforms for mD graph signals defined on Cartesian product graphs, including two-dimensional graph linear canonical transforms (2D GLCTs) based on adjacency matrices and graph Laplacian matrices. Furthermore, these transforms are extended to mD GLCTs, enabling the handling of more complex mD graph data. To demonstrate the practicality of the proposed method, this paper uses the 2D GLCT based on the Laplacian matrix as an example to detail its application in data compression.