Solving large-scale general phase retrieval problems via a sequence of convex relaxations

Reinier Doelman*, Thao Nguyen, Michel Verhaegen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)
55 Downloads (Pure)


We present a convex relaxation-based algorithm for large-scale general phase retrieval problems. General phase retrieval problems include, e.g., the estimation of the phase of the optical field in the pupil plane based on intensity measurements of a point source recorded in the image (focal) plane. The non-convex problem of finding the complex field that generates the correct intensity is reformulated into a rank constraint problem. The nuclear norm is used to obtain the convex relaxation of the phase retrieval problem. A new iterative method referred to as convex optimization-based phase retrieval (COPR) is presented, with each iteration consisting of solving a convex problem. In the noise-free case and for a class of phase retrieval problems, the solutions of the minimization problems converge linearly or faster towards a correct solution. Since the solutions to nuclear norm minimization problems can be computed using semidefinite programming, and this tends to be an expensive optimization in terms of scalability, we provide a fast algorithm called alternating direction method of multipliers (ADMM) that exploits the problem structure. The performance of the COPR algorithm is demonstrated in a realistic numerical simulation study, demonstrating its improvements in reliability and speed with respect to state-of-the-art methods.

Original languageEnglish
Pages (from-to)1410-1419
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Issue number8
Publication statusPublished - 2018


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