Leveraging prior knowledge in phase retrieval via Wirtinger Flows: from theory to practice

Thursday, August 17, 2017 - 9:00am - 9:45am
Lind 305
Mahdi Soltanolkotabi (University of Southern California)
This talk focuses on nonconvex gradient based methods (a.k.a. Wirtinger Flows) for solving phase retrieval problems. I will discuss results demonstrating that projected Wirtinger Flows, when initialized in a neighborhood of the desired signal, converge to the unknown signal at a linear rate. These results hold when prior knowledge is available in the form of closed sets (convex or nonconvex) providing convergence guarantees to the global optimum even when the objective function and constraint set is nonconvex. Furthermore, these results hold with a number of randomized measurements that is only a constant factor away from the minimal number of measurements required to uniquely identify the unknown signal. These results provide the first provably tractable algorithm for this data-poor regime, breaking local sample complexity barriers that have emerged in recent literature. I will also provide some preliminary theoretical results demonstrating the convergence of Wirtinger Flow-based methods to stationary points that hold for any measurement model despite the nonconvex and non-differentiable nature of the loss function. I will also introduce a new accelerated form of Wirtinger Flow that is able to escape low-quality local optima and achieve state of the art reconstruction results with less computational effort when
compared with classical baselines. Finally, I will discuss applications in the context of Ptychographic phaseless imaging of integrated circuits, demonstrating the ability of Wirtinger Flows to reconstruct nano-scale features in the presence of noise and device mis-alignments.

Parts of this talk is based on joint work with collaborators that will be probably introduced during the talk.