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

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