Generalized Graph Signal Reconstruction via the Uncertainty Principle

TL;DR

This paper develops a new uncertainty principle for graph signals, enabling better signal reconstruction in networks with incomplete data by balancing localization in vertex-time and spectral-frequency domains.

Contribution

It introduces a unified uncertainty framework for graph signals and constructs a joint vertex-time dictionary for improved reconstruction under practical constraints.

Findings

Enhanced reconstruction accuracy on real-world datasets

Improved noise robustness over existing methods

Effective signal localization in both domains

Abstract

We introduce a novel uncertainty principle for generalized graph signals that extends classical time-frequency and graph uncertainty principles into a unified framework. By defining joint vertex-time and spectral-frequency spreads, we quantify signal localization across these domains, revealing a trade-off between them. This framework allows us to identify a class of signals with maximal energy concentration in both domains, forming the fundamental atoms for a new joint vertex-time dictionary. This dictionary enhances signal reconstruction under practical constraints, such as incomplete or intermittent data, commonly encountered in sensor and social networks. Numerical experiments on real-world datasets demonstrate the effectiveness of the proposed approach, showing improved reconstruction accuracy and noise robustness compared to existing methods.