title: Proximity operators for phase retrieval.
abstract: 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 under-sampled 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 always perform better than using the classical intensity projector, while their computational overhead is moderate.
authors.forename: Ferréol
authors.initials: F
authors.lastname: Soulez
authors.forename: Éric
authors.initials: É
authors.lastname: Thiébaut
authors.forename: Antony
authors.initials: A
authors.lastname: Schutz
authors.forename: André
authors.initials: A
authors.lastname: Ferrari
authors.forename: Frédéric
authors.initials: F
authors.lastname: Courbin
authors.forename: Michael
authors.initials: M
authors.lastname: Unser