Multi-dimensional graph fractional Fourier transform and its application

TL;DR

This paper introduces a novel multi-dimensional graph fractional Fourier transform (MGFRFT) for analyzing signals on Cartesian product graphs, demonstrating its advantages in spectral analysis and data compression.

Contribution

It defines the MGFRFT based on Laplacian and adjacency matrices, exploring its properties and applications in multi-dimensional signal processing.

Findings

MGFRFT effectively captures the spectrum of multi-dimensional signals.

The transform improves computational efficiency in processing multi-dimensional data.

Application to data compression shows enhanced performance.

Abstract

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.