针对带恒定源项的图信号动态系统，提出随机时空采样方法实现稳定恢复。
Randomized Space-Time Sampling for Affine Graph Dynamical Systems
- 设计两种随机时空采样策略，适配非对角化系统矩阵
- 建立基于RIP的采样复杂度下界，确保初始状态与源项可稳定恢复
- 适用于图信号处理、动态系统建模，尤其适合源项未知场景
本文研究受恒定源项影响的图信号动态采样问题。信号在图上按线性动力系统随时间演化，初始状态和源项均为带限信号。提出两种随机时空采样方案，并分析稳定恢复的条件。相较于以往同质动态系统的研究，本框架引入恒定源项，导致系统矩阵不可对角化，经典谱方法失效，带来采样设计、稳定性分析及联合恢复的新挑战。分析核心为谱图加权相干性，刻画采样分布与图结构的关系。建立基于受限等距性质（RIP）的采样复杂度边界，并提出具理论误差保证的鲁棒恢复算法。在合成与真实数据集上通过大量实验验证了方法有效性。
原文摘要 · Abstract (English)
This paper investigates the problem of dynamical sampling for graph signals influenced by a constant source term. We consider signals evolving over time according to a linear dynamical system on a graph, where both the initial state and the source term are bandlimited. We introduce two random space-time sampling regimes and analyze the conditions under which stable recovery is achievable. While our framework extends recent work on homogeneous dynamics, it addresses a fundamentally different setting where the evolution includes a constant source term. This results in a non-orthogonal-diagonalizable system matrix, rendering classical spectral techniques inapplicable and introducing new challenges in sampling design, stability analysis, and joint recovery of both the initial state and the forcing term. A key component of our analysis is the spectral graph weighted coherence, which characterizes the interplay between the sampling distribution and the graph structure. We establish sampling complexity bounds ensuring stable recovery via the Restricted Isometry Property (RIP), and develop a robust recovery algorithm with provable error guarantees. The effectiveness of our method is validated through extensive experiments on both synthetic and real-world datasets.
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