# Randomized Space-Time Sampling for Affine Graph Dynamical Systems

arXiv: https://arxiv.org/abs/2509.16818 · HTML: https://mlsanity.com/paper/2509.16818/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 56 references that are in the map.
- First posted on arXiv 20 Sep 2025.

## Builds on (most cited first, 9 of 9)

- [Discrete Signal Processing on Graphs: Sampling Theory](https://mlsanity.com/paper/1503.05432/) (2015)
- [Sampling of graph signals with successive local aggregations](https://mlsanity.com/paper/1504.04687/) (2015)
- [Reconstruction of Time-varying Graph Signals via Sobolev Smoothness](https://mlsanity.com/paper/2207.06439/) (2022)
- [Random sampling of bandlimited signals on graphs](https://mlsanity.com/paper/1511.05118/) (2015)
- [Greedy Sampling of Graph Signals](https://mlsanity.com/paper/1704.01223/) (2017)
- [Localized Iterative Methods for Interpolation in Graph Structured Data](https://mlsanity.com/paper/1310.2646/) (2013)
- [Three-dimensional signal processing: a new approach in dynamical sampling via tensor products](https://mlsanity.com/paper/2502.02684/) (2025)
- [Sampling the flow of a bandlimited function](https://mlsanity.com/paper/2004.14032/) (2020)
- [Signal Recovery on Graphs: Random versus Experimentally Designed Sampling](https://mlsanity.com/paper/1504.05427/) (2015)

## Abstract (arXiv)

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.