Tirza Routtenberg

Sensor placement plays a crucial role in graph signal recovery in underdetermined systems. In this paper, we present the graph-filtered regularized maximum likelihood (GFR-ML) estimator of graph signals, which integrates general graph filtering with regularization to enhance recovery performance under a limited number of sensors. Then, we investigate task-based sampling allocation aimed at minimizing the mean squared error (MSE) of the GFR-ML estimator by optimizing sensor locations. Since this MSE depends on the unknown graph signals to be estimated, we propose four cost functions for the sampling allocation optimization: the biased Cramér-Rao bound (bCRB), the worst-case MSE (WC-MSE), the Bayesian MSE (BMSE), and the worst-case BMSE (WC-BMSE), where the Bayesian criteria assume a Gaussian prior. We investigate the properties of these cost functions and develop two algorithms for their practical implementation: 1) the straightforward greedy algorithm; and 2) the alternating projection gradient descent (PGD) algorithm, which reduces the computational complexity in large-scale settings and scales favorably with the graph size. Simulation results on synthetic and real-world datasets, including the IEEE 118-bus system, the METR-LA traffic network, the Minnesota road graph, and the Intel Lab wireless sensor network (WSN) dataset, demonstrate that, in the tested scenarios, the proposed sampling allocation methods reduce the MSE by up to 50% compared to standard sampling methods. Thus, the proposed methods improve the estimation performance and reduce the required number of measurements in graph signal processing (GSP)-based signal recovery in the case of underdetermined systems.