2025/09/20 by Le Le Gong, Gong, Le, Longxiu Huang +1 · 1 citation
Computer Science · Medicine · #Data-Driven Disease Surveillance #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Information Theory (cs.IT) #Machine Learning (cs.LG) #Medical Imaging Techniques and Applications #Numerical Analysis (math.NA) #Systems and Control (eess.SY) #Topological and Geometric Data Analysis #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2509.16818
openalex publication_date 2025/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.