Date of Award

Fall 2023

Project Type


Program or Major

Applied Mathematics

Degree Name

Doctor of Philosophy

First Advisor

Mark E Lyon

Second Advisor

Gregory P Chini

Third Advisor

Marek Petrik


In recent years, deep learning (DL) has become an increasingly important tool for many different types of classification, identification, and related problems including inverse radar and sonar applications. This thesis studies the degree to which radar and sonar systems may be optimized for DL algorithms in a theoretical setting. Most of the current existing literature found on using DL involve solving a full inverse scattering problem (ISP), that is to determine the properties and/or geometry of the scatter from nearly complete measurements of the scattered field. Methods suitable for use in two-dimensional space have been proposed and demonstrated with varying accuracies. In this work, we simplify the problem to only identifying objects in a previously collected catalog, which allows for accurate geometry classification with far less data.

To produce a data set suitable for deep learning, we obtain frequency domain far-field solutions corresponding to known geometries by means of a recently developed fast three-dimensional scattering solver. The scattered fields are then modulated using a multitude of learnable waveforms to identify frequencies for which learning/training is optimal. A major result of this research is its ability to identify an optimal radar/sonar signal that can be transmitted, which maximizes a DL algorithm’s ability to correctly identify any potential scattering obstacles. By assuming that the set of object geometries/scatterers is known (although the orientation of the scatterer to the incident field is still considered unknown), accurate identification is possible under more realistic conditions than is possible with current inverse scattering algorithms.

For instance, we show that collecting just the back-scattered far-field data is sufficient (which only assumes the radar source can also receive the scattered signal as opposed to typical ISP algorithms which depend on many different signal receivers surrounding the target in all directions). Normally distributed noise is also introduced during training as a means of regularization, to explore different waveforms that a deep learning optimizer may gravitate towards, and as a way to more accurately simulate real-world conditions where collected data may be imperfect. In military radar applications, this work is applicable in the sense that if a catalog of enemy aircraft exists, i.e. there is no need for a generalized reconstruction of the target geometry, one can simply classifying the enemy aircraft based off the return signal. The outcome of this work could potentially aid in the design and implementation of future advanced DL-based radar and sonar detection systems.