Multiple Hypothesis Testing Framework for Spatial Signals
This work addresses the challenge of spatial signal detection for applications like sensor networks, but it appears incremental as it builds on existing multiple hypothesis testing methods with a new estimation technique.
The authors tackled the problem of identifying spatially interesting or adversarial regions in distributed sensor networks by developing a multiple hypothesis testing framework that controls false discovery rates, using a novel data-driven method based on spectral moments to estimate local false discovery rates without relying on specific propagation models, and demonstrated its application to radio wave propagation.
The problem of identifying regions of spatially interesting, different or adversarial behavior is inherent to many practical applications involving distributed multisensor systems. In this work, we develop a general framework stemming from multiple hypothesis testing to identify such regions. A discrete spatial grid is assumed for the monitored environment. The spatial grid points associated with different hypotheses are identified while controlling the false discovery rate at a pre-specified level. Measurements are acquired using a large-scale sensor network. We propose a novel, data-driven method to estimate local false discovery rates based on the spectral method of moments. Our method is agnostic to specific spatial propagation models of the underlying physical phenomenon. It relies on a broadly applicable density model for local summary statistics. In between sensors, locations are assigned to regions associated with different hypotheses based on interpolated local false discovery rates. The benefits of our method are illustrated by applications to spatially propagating radio waves.