Dynamic Multiple-Parameter Joint Time-Vertex Fractional Fourier Transform and its Intelligent Filtering Methods

TL;DR

This paper introduces a novel dynamic multiple-parameter joint time-vertex fractional Fourier transform that adaptively models complex, time-varying graph signals and improves filtering performance in dynamic graph and video data.

Contribution

It proposes a new transform with time-varying fractional parameters for flexible spectral modeling of dynamic graph signals, along with two filtering methods for signal restoration.

Findings

Effective in capturing temporal topology variations.

Outperforms existing transforms and neural networks in denoising and deblurring.

Demonstrated on dynamic graph and video datasets.

Abstract

Dynamic graph signal processing provides a principled framework for analyzing time-varying data defined on irregular graph domains. However, existing joint time-vertex transforms such as the joint time-vertex fractional Fourier transform assign only one fractional order to the spatial domain and another one to the temporal domain, thereby restricting their capacity to model the complex and continuously varying dynamics of graph signals. To address this limitation, we propose a novel dynamic multiple-parameter joint time-vertex fractional Fourier transform (DMPJFRFT) framework, which introduces time-varying fractional parameters to achieve adaptive spectral modeling of dynamic graph structures. By assigning distinct fractional orders to each time step, the proposed transform enables dynamic and flexible representation of spatio-temporal signal evolution in the joint time-vertex spectral domain. Theoretical properties of the DMPJFRFT are systematically analyzed, and two filtering approaches: a gradient descent-based method and a neural network-based method, are developed for dynamic signal restoration. Experimental results on dynamic graph and video datasets demonstrate that the proposed framework effectively captures temporal topology variations and achieves superior performance in denoising and deblurring tasks compared with some state-of-the-art graph-based transforms and neural networks.