We investigate the dynamical sampling space-time trade-off problem within a graph setting. Specifically, we derive necessary and sufficient conditions for space-time sampling that enable the reconstruction of an initial band-limited signal on a graph. Additionally, we develop and test numerical algorithms for approximating the optimal placement of sensors on the graph to minimize the mean squared error when recovering signals from time-space measurements corrupted by i.i.d.~additive noise. Our numerical experiments demonstrate that our approach outperforms previously proposed algorithms for related problems.

翻译：我们研究了图设定下的动态采样时空权衡问题。具体而言，我们推导了能够重构图上初始带限信号的时空采样必要与充分条件。此外，我们开发并测试了数值算法，用于近似求解图传感器的最优布局，以最小化从受独立同分布加性噪声污染的时空测量中恢复信号时的均方误差。数值实验表明，我们的方法优于先前提出的相关问题的算法。