Imaging geometric graphs using internal measurements

This article presents two topologically-motivated algorithms for reconstructing a metric graph from solutions to a wave equation on it. Our algorithms rely on narrowband and visibility measurements, and are therefore of considerable value to urban sensing applications. This is an advancement over the wideband methods traditionally used to study metric graphs. Our methodology exposes and separates the impact of the graph topology and geometry and is driven by a complete cohomological characterization of the space of wave equation solutions.