Space-Time Variable Density Samplings for Sparse Bandlimited Graph Signals Driven by Diffusion Operators
Space-Time Variable Density Samplings for Sparse Bandlimited Graph Signals Driven by Diffusion Operators
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DOI：
10.1109/icassp49357.2023.10095406
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发表时间：
2023-06
期刊：
影响因子：
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通讯作者：
Qing Yao;Longxiu Huang;Sui Tang
中科院分区：
文献类型：
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作者：
Qing Yao;Longxiu Huang;Sui Tang
我们考虑由热扩散过程驱动的稀疏带限图信号的时空采样和重构。在本文中，我们开发了一个抽样框架，包括随机选择一个小的时空节点的子集，根据一些概率分布，推广经典的变密度抽样的热扩散场。我们表明，确保稳定恢复所需的空间-时间样本的数量取决于由图形拓扑结构，时间动态和采样概率分布之间的相互作用确定的不相干参数。在最佳情况下，只要$\mathcal{O}\left（{s\log k} \right）$空时样本就足以确保精确恢复所有额外s-稀疏的k-带限图信号。我们提出的采样方法需要更少的空间样本比静态的情况下，利用时间信息。最后，我们测试我们的采样技术在各种各样的图。对人工气候数据和真实的气候数据的数值结果支持了我们的理论研究结果，并证明了其实用性。
We consider the space-time sampling and reconstruction of sparse bandlimited graph signals driven by a heat diffusion process. In this paper, we develop a sampling framework consisting of selecting a small subset of space-time nodes at random according to some probability distribution, generalizing the classical variable density sampling to the heat diffusion field. We show that the number of space-time samples required to ensure stable recovery depends on an incoherence parameter determined by the interplay between graph topology, temporal dynamics, and sampling probability distributions. In optimal scenarios, as few as $\mathcal{O}\left( {s\log k} \right)$ space-time samples are sufficient to ensure accurate recovery of all k-bandlimited graph signals that are additionally s-sparse. Our proposed sampling method requires much fewer spatial samples than the static case by leveraging temporal information. Finally, we test our sampling techniques on a wide variety of graphs. The numerical results on synthetic and real climate data sets support our theoretical findings and demonstrate the practical applicability.