Node sampling by partitioning on graphs via convex optimization

In this paper we deal with the problem of efficiently and accurately reconstructing a complete graph signal from partially observed noisy measurements. Given a graph structure, we propose a solution based on convex optimization techniques to partition the nodes of the graph into subsets such that sampling a graph signal from any of these subsets provides an accurate, low mean squared error for example, reconstruction of the original complete graph signal. We show how the proposed sampling set construction approach relates to optimal experimental design, sensor management, positioning and selection problems and provide numerical simulation results on synthetic and real-world graphs.