Multiple-Parameter Graph Fractional Fourier Transform: Theory and Applications

TL;DR

This paper introduces multiple-parameter graph fractional Fourier transforms (MPGFRFTs) with adaptive and learnable features, enabling improved spectral analysis, compression, denoising, and encryption of graph signals and images.

Contribution

It proposes novel MPGFRFTs with theoretical foundations, spectral compression strategies, and learnable order schemes for enhanced flexibility and performance in graph signal processing.

Findings

Effective spectral compression at ultra-low ratios

Superior denoising and compression performance

Successful application to image encryption and decryption

Abstract

The graph fractional Fourier transform (GFRFT) applies a single global fractional order to all graph frequencies, which restricts its adaptability to diverse signal characteristics across the spectral domain. To address this limitation, in this paper, we propose two types of multiple-parameter GFRFTs (MPGFRFTs) and establish their corresponding theoretical frameworks. We design a spectral compression strategy tailored for ultra-low compression ratios, effectively preserving essential information even under extreme dimensionality reduction. To enhance flexibility, we introduce a learnable order vector scheme that enables adaptive compression and denoising, demonstrating strong performance on both graph signals and images. We explore the application of MPGFRFTs to image encryption and decryption. Experimental results validate the versatility and superior performance of the proposed MPGFRFT framework across various graph signal processing tasks.