{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/proximity-operators-for-phase-retrieval","title":"Proximity Operators for Phase Retrieval","arxiv_id":"1710.10046","date":"2017-10-27","proceeding":null,"authors":["Ferréol Soulez","Éric Thiébaut","Antony Schutz","André Ferrari","Frédéric Courbin","Michael Unser"],"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 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.","url_abs":"http://arxiv.org/abs/1710.10046v1","url_pdf":"http://arxiv.org/pdf/1710.10046v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"proximity-operators-for-phase-retrieval","repo_url":"https://github.com/FerreolS/COMCI","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}