基于不确定性原理的广义图信号重建
Generalized Graph Signal Reconstruction via the Uncertainty Principle
AI总结：
本文提出广义图信号的新型不确定性原理，通过联合顶点-时间与频谱-频率展宽构建能量集中原子字典，以提升不完整或间歇数据下的信号重建精度与噪声鲁棒性。
摘要：
我们提出了一种适用于广义图信号的新型不确定性原理，将经典时频不确定性原理与图不确定性原理扩展到一个统一框架中。通过定义联合顶点-时间展宽和频谱-频率展宽，我们量化了信号在这些域中的局部化程度，揭示了二者之间的权衡。该框架使我们能够识别一类在两个域中均具有最大能量集中度的信号，从而构成新的联合顶点-时间字典的基本原子。该字典在不完整或间歇性数据等实际约束下增强了信号重建能力，这些约束常见于传感器网络和社交网络。在真实数据集上的数值实验证明了所提方法的有效性，结果表明，与现有方法相比，其重建精度和噪声鲁棒性均有所提升。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
