Title:  A Geometrical Variational Approach to Shape Inversion for Radar

Committee:

Dr. Anthony Yezzi, ECE, Chair , Advisor

Dr. Christopher Barnes, ECE

Dr. Aaron Lanterman, ECE

Dr. Patricio Vela, ECE

Dr. Thomas Orlando, Chemistry

Abstract:

In this thesis, we develop a novel method for dense shape reconstruction of scenes using radar. For a given scene and antennas taking measurements from the scene, our method iteratively estimates the scene shape using the measurements. To this end, we use a deformable shape evolution approach which seeks to match the received signal to a computed forward model based on the evolving shape. Adopting such an approach comes with important advantages such as the ability to naturally embed the shape priors into the estimation and being able to model self-occlusions which cannot be easily incorporated into classical radar imaging techniques. Iterations start with an initial shape which is gradually deformed until its image under the forward model gets sufficiently close to the actual measurements. Since we use a gradient-based scheme to minimize our error and radar signals are highly oscillatory, a special attention is required to prevent these oscillations to manifest in the cost functional as local minima. For this purpose, we develop a novel technique by which we can extract the geometric information embedded in the radar signals to that is used to formulate the cost functional. We test our approach with synthetic simulations performed in 2D which shows the promise of our approach on some challenging scenarios.