# Efficient Sampling Allocation Strategies for General Graph-Filter-Based Signal Recovery

arXiv: https://arxiv.org/abs/2502.05583 · HTML: https://mlsanity.com/paper/2502.05583/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2025.

## Built on by (most cited first, 1 of 1)

- [Cramer-Rao Bounds for Laplacian Matrix Estimation](https://mlsanity.com/paper/2504.04576/) (2025)

## Abstract (arXiv)

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 signal 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 wisely choosing sensor placement. Since this MSE depends on the unknown graph signals to be estimated, we propose four cost functions for the optimization of the sampling allocation: the biased Cramacuteer-Rao bound (bCRB), the worst-case MSE (WC-MSE), the Bayesian MSE (BMSE), and the worst-case BMSE (WC-BMSE), where the last two 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 that reduces the computational complexity. Simulation results on synthetic and real-world datasets of the IEEE 118-bus power system and the Minnesota road network demonstrate that, in the tested scenarios, the proposed sampling allocation methods reduce the MSE by up to 50% compared to the common sampling methods A-design, E-design, and LR-design. 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.