UC Berkeley

In many physical settings, it is difficult or impossible to measure the phase of a signal. The problem is then to recover a signal from intensity measurements only. This phase retrieval problem has challenged physicists, mathematicians and engineers for decades, being notoriously difficult to solve numerically. We propose a novel framework for phase retrieval, which recasts the problem as a low rank matrix recovery problem and provide theoretical guarantees and empirical demonstrations of its performance, as well as connections of our results to quantum mechanics and random matrix theory.