Characterizing High-Dimensional Optical Systems with Applications in Compressive Sensing and Quantum Data Locking
Daniel J. Lum · arXiv (Cornell University) · 2018
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.