Trajectory invariant representations of synthetic aperture sonar data

The topology of the signature space of a circular synthetic aperture sonar or radar collection is highly constrained. Intuitively, strong constraints on the signature space ensure that certain physical properties of a target will translate into its topological structure.

This talk presents a strong connection between the physical acoustics of an object and the topology of the space of sonar echoes resulting from a circular synthetic aperture sonar (CSAS) collection of that object. A simple theoretical model is developed that yields a precise, yet qualitative, description of the space of echoes. This theoretical model is validated in simulation and with experimental data from a laboratory sonar system.

Ultimately, this talk shows that there are distinct topological and geometric features in the signature and phase spaces are that are reflected in their corresponding persistent homology diagrams. These features appear to correspond directly to the raw sonar data, and by extension relate to the physical acoustics of the targets. Moreover, the features are mathematical categories, which yields some interesting structural insights.

This is joint work with Zander Memon and was partially funded by ONR.