Observing Bandlimited Graph Processes from Subsampled Measurements
Elvin Isufi (TU Delft - Electrical Engineering, Mathematics and Computer Science, Università degli Studi di Perugia)
Paolo Banelli (Università degli Studi di Perugia)
Paolo Di Lorenzo (Sapienza University of Rome)
Geert Leus (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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Abstract
This work merges tools from graph signal processing and linear systems theory to propose sampling strategies for observing the initial state of a process evolving over a graph. The proposed method is ratified by a mathematical analysis that provides insights on the role played by the different actors, such as the graph topology, the process bandwidth, and the sampling strategy. Moreover, conditions when the graph process is observable from a few samples and (sub)optimal sampling strategies that jointly exploit the nature of the graph structure and graph process are proposed. Finally, numerical tests are conducted to illustrate the benefits of the proposed approach.