  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.
