{"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/conjugate-phase-retrieval-in-paley-wiener","title":"Conjugate Phase Retrieval in Paley-Wiener Space","arxiv_id":"1910.12975","date":"2019-10-28","proceeding":null,"authors":["Chun-Kit Lai","Friedrich Littmann","Eric Weber"],"abstract":"We consider the problem of conjugate phase retrieval in Paley-Wiener space $PW_{\\pi}$. The goal of conjugate phase retrieval is to recover a signal $f$ from the magnitudes of linear measurements up to unknown phase factor and unknown conjugate, meaning $f(t)$ and $\\overline{f(t)}$ are not necessarily distinguishable from the available data. We show that conjugate phase retrieval can be accomplished in $PW_{\\pi}$ by sampling only on the real line by using structured convolutions. We also show that conjugate phase retrieval can be accomplished in $PW_{\\pi}$ by sampling both $f$ and $f^{\\prime}$ only on the real line. Moreover, we demonstrate experimentally that the Gerchberg-Saxton method of alternating projections can accomplish the reconstruction from vectors that do conjugate phase retrieval in finite dimensional spaces. Finally, we show that generically, conjugate phase retrieval can be accomplished by sampling at three times the Nyquist rate, whereas phase retrieval requires sampling at four times the Nyquist rate.","url_abs":"http://arxiv.org/abs/1910.12975v1","url_pdf":"http://arxiv.org/pdf/1910.12975v1.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":"conjugate-phase-retrieval-in-paley-wiener","repo_url":"https://bitbucket.org/esweber/conjugate-phase-retrieval","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}