Recent algorithmic advances in Phase Retrieval
Jonathan Dong

Meeting • 22 December 2020

Abstract
Phase Retrieval is a longstanding problem in imaging, arising in astronomy, microscopy, or computer-generated holography. This non-linear equation y = |Ax|² is non-convex and difficult to solve, with many different algorithms proposed in physics. On the other hand, this equation may also be seen as the simplest form of non-linear neural network, a one-layer network with quadratic activation. This observation has generated a considerable amount of theoretical studies in the past 5 years to understand this computational problem better. In particular, two new classes of algorithms have been developed in my previous group and will be presented, spectral methods and Approximate-Message Passing. I apologize in advance for the absence of splines in this presentation, but hope we can find a remedy together in future research projects.