Topological and geometric characterization of synthetic aperture sonar collections

TL;DR

This paper investigates the topological and geometric features of synthetic aperture sonar data, providing theoretical guarantees about the structure of echo signatures relevant for classification, with practical implications demonstrated in laboratory conditions.

Contribution

It offers a novel theoretical framework for understanding the structure of sonar echo data, with minimal assumptions on platform trajectory and measurable features for classification.

Findings

The signature space divides into topological features based on echo count and placement.

Geometric features effectively capture sonar cross sections.

Theoretical guarantees hold under laboratory conditions.

Abstract

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.