Sensor networks and inverse scattering

We consider a wired network of analog sensors in one dimension. Each sensor measures some physical quantity and "communicates" with its adjacent neighbors. The base station can access the network by communicating with the sensors at the boundaries. We show that by making measurements at the boundary (i.e. from the first sensor) we can determine the values of the unknown field values along the entire network stably. The method is based on building an analogy with classical one dimensional inverse scattering (Helmholtz equation) for which the Chen-Rokhlin algorithm provides a highly surprising stable method for recovering the scattering parameters. Simulation results validating the scheme for thousands of sensors are presented.