任意图信号Hilbert空间的顶点采样
Graph Vertex Sampling with Arbitrary Graph Signal Hilbert Spaces
摘要：
图顶点采样集选择的目的是选择一组图的顶点，使得仅从这些样本可以精确重构的图信号的空间是最大的。在这种情况下，我们建议扩展采样集选择的频谱代理的基础上，任意希尔伯特空间的图形信号。启用图形信号的任意内积允许随后更好地考虑图形上的顶点重要性以用于适于应用的采样。我们首先说明内积的变化如何影响采样集的选择和重建，然后将其应用于几何图形的背景下，以突出如何选择替代的内积矩阵可以帮助采样集的选择和重建。
英文摘要：
Graph vertex sampling set selection aims at selecting a set of ver-tices of a graph such that the space of graph signals that can be reconstructed exactly from those samples alone is maximal. In this context, we propose to extend sampling set selection based on spectral proxies to arbitrary Hilbert spaces of graph signals. Enabling arbitrary inner product of graph signals allows then to better account for vertex importance on the graph for a sampling adapted to the application. We first state how the change of inner product impacts sampling set selection and reconstruction, and then apply it in the context of geometric graphs to highlight how choosing an alternative inner product matrix can help sampling set selection and reconstruction.
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