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) .

Authors:

Felix Krahmer (Technical University of Munich, Department of Mathematics)

Yi-Kai Liu (National Institute of Standards and Technology)

Keywords:

image reconstruction, phase retrieval, stochastic processes