Phase Retrieval Without Small-Ball Probability AssumptionsMS21

It is well known that many classes of random embeddings (e.g., Bernoulli matrices) do not allow for recovery from phaseless measurements. In this talk will discuss that there is still a large class of signals that can be reconstructed uniquely, namely "non-peaky" ones. We will discuss stability and uniqueness as well as a uniform recovery guarantee for the PhaseLift algorithm. In all of these cases, the number of measurements m approaches the information-theoretic lower bound.

This presentation is part of Minisymposium “MS21 - Recent mathematical advances in phase retrieval and computational imaging (2 parts)
organized by: Mahdi Soltanolkotabi (University of Southern California) , Tamir Bendory (Princeton University) .

Felix Krahmer (Technical University of Munich, Department of Mathematics)
Yi-Kai Liu (National Institute of Standards and Technology)
image reconstruction, phase retrieval, stochastic processes