Hicks, Illya2019-05-172019-05-172018-122019-04-11December 2Leong, Oscar. "Phase Retrieval Under a Generative Prior." (2019) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/105890">https://hdl.handle.net/1911/105890</a>.https://hdl.handle.net/1911/105890The phase retrieval problem, arising from X-ray crystallography and medical imaging, asks to recover a signal given intensity-only measurements. When the number of measurements is less than the dimensionality of the signal, solving the problem requires additional assumptions, or priors, on its structure in order to guarantee recovery. Many techniques enforce a sparsity prior, meaning that the signal has very few non-zero entries. However, these methods have seen various computational bottlenecks. We sidestep this issue by enforcing a generative prior: the assumption that the signal is in the range of a generative neural network. By formulating an empirical risk minimization problem and directly optimizing over the domain of the generator, we show that the objective’s energy landscape exhibits favorable global geometry for gradient descent with information theoretically optimal sample complexity. Based on this geometric result, we introduce a gradient descent algorithm to converge to the true solution. We corroborate these results with experiments showing that exploiting generative models in phase retrieval tasks outperforms sparse phase retrieval methods.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Phase RetrievalGenerative ModelsNon-convex OptimizationDeep LearningThesis2019-05-17