My dissertation research is on an eigenvalue optimization method for phase retrieval. The code and experiment files for this phase retrieval method can be found at GitHub.com/Will-Wright/low-rank-opt-rapid-eig.
I have also studied and implemented efficient methods for image segmentation, lasso/basis pursuit, and quadratic programming which can be found at my main GitHub page.
Dissertation Abstract: Phase retrieval is the process of recovering the phase of an unknown signal using only the magnitudes of some signal observations. Some common applications are X-ray crystallography, electron microscopy, speech processing, and astronomical imaging. A wide variety of methods exist for retrieving phase, yet most do not allow for much noise in the observations. A phase retrieval method was recently developed by [Friedlander et al, 2016] which handles noise, leading to an eigenvalue optimization problem. This underlying eigenvalue problem has a unique structure which we exploit using modern eigenvalue methods to increase the efficiency of the phase retrieval process.