Characterizing High-Dimensional Optical Systems with Applications in Compressive Sensing and Quantum Data Locking

Abstract

This University of Rochester Physics Ph.D. dissertation introduces concepts in compressive sensing, quantum entanglement, FMCW LiDAR, and quantum data locking. Additionally, the appendix serves as a thorough reference for those interested in applying the alternating direction method of multipliers (ADMM) to optimize an augmented Lagrangian and can easily be tailored to specific optimization problems. In particular, I show how fast Hadamard transforms and the ADMM can be used for $L^1$-minimization with different sparse-basis transforms along with total-variation minimization of both images and video. The simple examples given demonstrate how to minimize high-dimensional problems with little memory overhead. The original version of this dissertation can be accessed through ProQuest.