Efficient Sampling Allocation Strategies for General Graph-Filter-Based Signal Recovery
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 Cram$\acute{\text{e}}$r-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 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 in the tested scenarios. 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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Fast Resampling of 3D Point Clouds via Graphs
To reduce cost in storing, processing and visualizing a large-scale point cloud, we consider a randomized resampling strategy to select a representative subset of points while preserving application-dependent features. T…
Sampling Policy Design for Tracking Time-Varying Graph Signals with Adaptive Budget Allocation
There have been many works that focus on the sampling set design for a static graph signal, but few for time-varying graph signals (GS). In this paper, we concentrate on how to select vertices to sample and how to alloca…
Graph Signal Sampling Under Stochastic Priors
We propose a generalized sampling framework for stochastic graph signals. Stochastic graph signals are characterized by graph wide sense stationarity (GWSS) which is an extension of wide sense stationarity (WSS) for stan…
On Sampling Strategies for Neural Network-based Collaborative Filtering
Recent advances in neural networks have inspired people to design hybrid recommendation algorithms that can incorporate both (1) user-item interaction information and (2) content information including image, audio, and t…
Collaborative FilteringMulti-channel Sampling on Graphs and Its Relationship to Graph Filter Banks
In this paper, we consider multi-channel sampling (MCS) for graph signals. We generally encounter full-band graph signals beyond the bandlimited one in many applications, such as piecewise constant/smooth and union of ba…