Topological and geometric characterization of synthetic aperture sonar collections

This article explores the theoretical underpinnings of -- and practical results for -- topological and geometric features of data collected by synthetic aperture sonar systems. We prove a strong theoretical guarantee about the structure of the space of echos (the signature space) that is relevant for classification, and that this structure is measurable in laboratory conditions. The guarantee makes minimal assumptions about the sonar platform's trajectory, and establishes that the signature space divides neatly into topological features based upon the number of prominent echos and their placement, and geometric features that capture their corresponding sonar cross section.