Multi-dimensional graph fractional Fourier transform and its application

Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of graph signal processing. This paper investigates the novel transform for multi-dimensional signals defined on Cartesian product graph and studies several related properties. Our work includes: (i) defining the multi-dimensional graph fractional Fourier transform (MGFRFT) based on Laplacian matrix and adjacency matrix; (ii) exploring the advantages of MGFRFT in processing multi-dimensional signals in terms of spectrum and computational time; (iii) applying the proposed transform to data compression to highlight the utility and effectiveness of it.