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Data-Driven Discovery of Linear Dynamical Systems Over Graphs via Dynamical Sampling
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- 1 Intro
- 2 Graph signal processing Given information at a subset nodes of a graph, can we recover the missing information on other modes in a robust and efficient way?
- 3 Preliminaries
- 4 Sampling of graph signals
- 5 Motivation
- 6 Relation to Frame/Basis theory in Harmonic analysis
- 7 Previous work on deterministic dynamical sampling
- 8 Relation to linear inverse problem How to choose space-time samples that can do as good as spatial samples? Formulation We can write the space-time sampling as
- 9 Randomized dynamical sampling We propose three different random space-time sampling regimes
- 10 Random space-time sampling model
- 11 Connection with the static case T=1
- 12 Optimal sampling distributions
- 13 Summary • Optimal sampling distribution depends on the graph structure and the
- 14 Reconstruction strategy
- 15 Guarantees for standard decoder
- 16 Guarantees for efficient decoder
- 17 System Identification in dynamical sampling
- 18 Generalization to affine systems
- 19 Numerical Results
