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

TL;DR

This dissertation explores high-dimensional optical systems, applying compressive sensing and quantum techniques, and introduces optimization methods like ADMM for efficient data processing in quantum and imaging applications.

Contribution

It introduces novel applications of ADMM and fast Hadamard transforms for high-dimensional optimization in quantum data locking and compressive sensing.

Findings

Effective use of ADMM for $L^1$-minimization

Application of fast Hadamard transforms in sparse recovery

Demonstrated low-memory high-dimensional optimization

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.