Compressed sensing for phase retrieval.

To date there are several iterative techniques that enjoy moderate success when reconstructing phase information, where only intensity measurements are made. There remains, however, a number of cases in which conventional approaches are unsuccessful. In the last decade, the theory of compressed sensing has emerged and provides a route to solving convex optimisation problems exactly via ℓ(1)-norm minimization. Here the application of compressed sensing to phase retrieval in a nonconvex setting is reported. An algorithm is presented that applies reweighted ℓ(1)-norm minimization to yield accurate reconstruction where conventional methods fail.