论文标题
使用任意图信号希尔伯特空间的图形顶点采样
Graph Vertex Sampling with Arbitrary Graph Signal Hilbert Spaces
论文作者
论文摘要
Graph Pertex采样集选择旨在选择图形的一组vertices，以便可以单独从这些样品中精确重建的图形信号的空间是最大的。在这种情况下，我们建议将基于光谱代理的采样集进行选择，以扩展到图形信号的任意希尔伯特空间。启用图形信号的任意内部乘积可以更好地说明适合应用程序的采样的图表上的顶点的重要性。我们首先说明内部产品的变化如何影响采样集选择和重建，然后在几何图的背景下应用它，以突出显示选择替代性内部产品矩阵如何帮助采样设置选择和重建。
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.
