# Generalized Graph Signal Reconstruction via the Uncertainty Principle

arXiv: https://arxiv.org/abs/2409.04229 · HTML: https://mlsanity.com/paper/2409.04229/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2024.

## Built on by (most cited first, 2 of 2)

- [HeteroBA: A Structure-Manipulating Backdoor Attack on Heterogeneous Graphs](https://mlsanity.com/paper/2505.21140/) (2025)
- [HeteroHBA: A Generative Structure-Manipulating Backdoor Attack on Heterogeneous Graphs](https://mlsanity.com/paper/2512.24665/) (2025)

## Abstract (arXiv)

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.