Proximity Operators for Phase Retrieval

We present a new formulation of a family of proximity operators that generalize the projector step for phase retrieval. These proximity operators for noisy intensity measurements can replace the classical "noise free" projection in any projection-based algorithm. They are derived from a maximum likelihood formulation and admit closed form solutions for both the Gaussian and the Poisson cases. In addition, we extend these proximity operators to undersampled intensity measurements. To assess their performance, these operators are exploited in a classical Gerchberg Saxton algorithm. We present numerical experiments showing that the reconstructed complex amplitudes with these proximity operators perform always better than using the classical intensity projector while their computational overhead is moderate.