Sampling Limits for Detection and Identification in Sensor Networks
Galen Reeves and Michael Gastpar
Sensor networks perform a spatio-temporal sampling of the environment, and a natural question concerns the relationship between the sampling density and the resulting insight one can gain into the environment. Such questions are often considered from the perspective of recovering the underlying signal of interest, either perfectly or within a small squared error. However, many of the most interesting sensor network applications will not require such a reconstruction. Rather, for tasks such as detection and identification, only certain basic facts about the environment are of interest. Under different models of the environment and the measurement uncertainty, what are the limits on the sampling density to guarantee a certain level of fidelity in detection and identification?
In this project, we draw upon recent work in compressed sensing to analyze models where the properties of interest are sparse or somehow compressible, and are sampled using randomly constructed linear projections. Additionally, we consider the affects of communication constraints within the sensor network.