Phase retrieval problems consist in recovering elements of a complex vector space from the modulus of their scalar product with a fixed family of measurement vectors. Traditional reconstruction algorithms rely on simple local optimization heuristics. Although they can in principle, because of the non-convexity of the problem, get stuck in local optima, they are observed to work well in many situations.
In this talk, we will see which theoretical correctness guarantees one can establish, in a particular setting, for the most well-known such algorithm. We will also present a different family of algorithms, based on so-called convexification techniques, describe its advantages and limitations.