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Ph.D. Dissertation Defense - Nicholas Bertrand

Event Details

Wednesday, October 30, 2019

12:30pm - 2:30pm

Location: 
C-1315, CODA

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Event Details

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

Committee:

Dr. Christopher Rozell, ECE Advisor

Dr. Mark Davenport, ECE

Dr. Adam Charles

Dr. Omer Inan, ECE

Dr. Samuel Shapero

Abstract: The objective of this 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 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, wavefront, and frequency tracking scenarios with applications to electrophysiology. Next, we utilize optimal transport formulations to build on other types of structure by regularizing the sparse plus low rank problem in robust principle components analysis. This approach is validated through simulations on natural and infrared video sequences. Finally, we study 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.

Last revised October 18, 2019