Title:  Exploiting Structure in Dynamical Systems for Tracking and Dimensionality Reduction

Committee: 

Dr. Rozell, Advisor       

Dr. Davenport, Chair

Dr. Dyer

Abstract:

The objective of the proposed research is to leverage the underlying structure in observations from dynamical systems to improve tracking performance and efficiently perform dimensionality reduction. First, we propose the use of the earth mover's distance (EMD) as a dynamics regularizer for sparse signal tracking. Traditional tracking algorithms such as the Kalman filter use the lp-norm to evaluate similarity between the signal estimate and prediction from the dynamics model. However, the lp-norm does not effectively exploit the geometric structure or ordering present in the coefficients in many applications such as imaging and frequency estimation. The EMD is a natural alternative dynamics regularizer which is inherently aware of the structure between elements by way of a user-defined cost matrix. In this work, we formulate an EMD-based tracking algorithm and evaluate its performance in imaging and frequency tracking scenarios with applications to electrophysiology. The second thrust of the proposed research studies an efficient dimensionality reduction scheme based on random projections for observations from a dynamical system which has converged to a low-dimensional attractor manifold. Performance is evaluated via tasks on synthetic neural imaging and fluid flow data. Finally, the proposed research will explore the challenging infrared search and track problem where the goal is to track small targets on a noisy background in images recorded from a moving platform. We propose to develop a tracking framework which incorporates a sparse plus low-rank model and an EMD dynamics regularizer. Performance will be evaluated on realistic infrared imagery simulations.