This paper addresses the problem of selecting an optimal sampling set for $K$ -bandlimited signals on graphs. The proposed sampling method is based on two proposed concepts of correlation quantity and effective node. First, we clarify the relationship between the uniqueness set and the effective node, and subsequently show that the effective node set selected by space division constitutes a uniqueness set for $K$ -bandlimited signals, thereby obtaining an efficient reconstruction method for $K$ -bandlimited signals. Then, to reduce the effect of noise, the proposed method finds an optimal sampling set by selecting the best node with the maximum correlation quantity in each node selection. Furthermore, we show that the proposed method can be performed for sampling $K$ -bandlimited signals by using an estimation eigenspace without computing the eigendecomposition of a variation operator. Finally, we compare our approach with other existing sampling approaches through comparisons of reconstruction error and running time to evaluate its performance.

中文翻译：

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图上采样带限信号的高效节点选择策略

本文解决了选择最优抽样集的问题 $K$ - 图上的带限信号。所提出的采样方法基于相关量和有效节点两个提出的概念。首先阐明唯一性集和有效节点的关系，然后证明空间划分选择的有效节点集构成了一个唯一性集$K$ -带限信号，从而获得一种有效的重建方法 $K$ -带限信号。然后，为了减少噪声的影响，所提出的方法通过在每个节点选择中选择具有最大相关量的最佳节点来寻找最优采样集。此外，我们表明所提出的方法可以用于采样$K$ -bandlimited 信号通过使用估计特征空间而不计算变异算子的特征分解。最后，我们通过比较重建误差和运行时间来评估其性能，将我们的方法与其他现有的采样方法进行比较。