Sampling of Graph Signals Based on Joint Time-Vertex Fractional Fourier Transform

TL;DR

This paper proposes a novel sampling method for graph signals using the joint time-vertex fractional Fourier transform, improving recovery and efficiency in time-varying data analysis.

Contribution

It introduces a new sampling theory based on JFRFT, including conditions for perfect recovery and strategies for optimal sampling set selection.

Findings

Achieves high recovery accuracy for jointly bandlimited signals

Demonstrates improved computational efficiency in large-scale processing

Validates methods with numerical simulations and real data experiments

Abstract

With the growing demand for non-Euclidean data analysis, graph signal processing (GSP) has gained significant attention for its capability to handle complex time-varying data. This paper introduces a novel sampling method based on the joint time-vertex fractional Fourier transform (JFRFT), enhancing signal representation in time-frequency analysis and GSP. The JFRFT sampling theory is established by deriving conditions for the perfect recovery of jointly bandlimited signals, along with an optimal sampling set selection strategy. To further enhance the efficiency of large-scale time-vertex signal processing, the design of localized sampling operators is investigated. Numerical simulations and real data experiments validate the superior performance of the proposed methods in terms of recovery accuracy and computational efficiency, offering new insights into efficient time-varying signal processing.