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arXiv · 2409.04229

Generalized Graph Signal Reconstruction via the Uncertainty Principle

Yanan Zhao·Xingchao Jian·Feng Ji·Wee Peng Tay·Antonio Ortega
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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.

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Yanan Zhao, Xingchao Jian, Feng Ji, Wee Peng Tay, Antonio Ortega. 2024-09-06. Generalized Graph Signal Reconstruction via the Uncertainty Principle. https://arxiv.org/abs/2409.04229

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