Topological and geometric characterization of synthetic aperture sonar collections

Michael Robinson; Zander Memon; Maxwell Gualtieri

doi:10.1121/10.0037085

Topological and geometric characterization of synthetic aperture sonar collections

J Acoust Soc Am. 2025 Jul 1;158(1):51-66. doi: 10.1121/10.0037085.

Authors

Michael Robinson¹, Zander Memon², Maxwell Gualtieri³

Affiliations

¹ Mathematics and Statistics, American University, Washington, DC 20016, USA.
² Department of Economics, University of California, Davis, California 95616, USA.
³ McCormick School of Engineering, Northwestern University, Evanston, Illinois 60208, USA.

PMID: 40600693
DOI: 10.1121/10.0037085

Abstract

This article explores the theoretical underpinnings of-and practical results for-topological and geometric features of data collected by synthetic aperture sonar systems. Under a reasonable structural assumption, we prove a 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. Aside from a baseline noise level estimate, our theoretical guarantee makes minimal assumptions about the trajectory of the sonar platform, and establishes that the signature space divides neatly into topological features based upon the number of prominent echos and their location within the scene, and geometric features that capture their corresponding echo amplitude.