论文标题
带有自适应预算分配的随时间变化的图形信号的采样策略设计
Sampling Policy Design for Tracking Time-Varying Graph Signals with Adaptive Budget Allocation
论文作者
论文摘要
有许多作品专注于静态图形信号的采样集设计，但对于随时间变化的图形信号（GS）很少。在本文中，我们专注于如何选择顶点进行采样以及如何为时间变化的GS分配采样预算，以实现长期的最小跟踪误差。在Kalman过滤器（KF）框架中，采样策略设计和预算分配的问题被提出为无限的地平线顺序决策过程，其中通过动态编程（DP）获得了最佳采样策略。由于最佳策略是棘手的，因此通过截断无限的地平线提出了近似算法。通过引入一种用于分析复合函数的凸度或凹形的新工具，我们证明了截断的问题是凸。最后，我们通过数值实验证明了所提出的方法的性能。
There have been many works that focus on the sampling set design for a static graph signal, but few for time-varying graph signals (GS). In this paper, we concentrate on how to select vertices to sample and how to allocate the sampling budget for a time-varying GS to achieve a minimal tracking error for the long-term. In the Kalman Filter (KF) framework, the problem of sampling policy design and budget allocation is formulated as an infinite horizon sequential decision process, in which the optimal sampling policy is obtained by Dynamic Programming (DP). Since the optimal policy is intractable, an approximate algorithm is proposed by truncating the infinite horizon. By introducing a new tool for analyzing the convexity or concavity of composite functions, we prove that the truncated problem is convex. Finally, we demonstrate the performance of the proposed approach through numerical experiments.
