{"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/fast-phase-retrieval-from-local-correlation","title":"Fast Phase Retrieval from Local Correlation Measurements","arxiv_id":"1501.02377","date":"2015-01-10","proceeding":null,"authors":["Mark Iwen","Aditya Viswanathan","Yang Wang"],"abstract":"We develop a fast phase retrieval method which can utilize a large class of local phaseless correlation-based measurements in order to recover a given signal ${\\bf x} \\in \\mathbb{C}^d$ (up to an unknown global phase) in near-linear $\\mathcal{O} \\left( d \\log^4 d \\right)$-time. Accompanying theoretical analysis proves that the proposed algorithm is guaranteed to deterministically recover all signals ${\\bf x}$ satisfying a natural flatness (i.e., non-sparsity) condition for a particular choice of deterministic correlation-based measurements. A randomized version of these same measurements is then shown to provide nonuniform probabilistic recovery guarantees for arbitrary signals ${\\bf x} \\in \\mathbb{C}^d$. Numerical experiments demonstrate the method's speed, accuracy, and robustness in practice -- all code is made publicly available. Finally, we conclude by developing an extension of the proposed method to the sparse phase retrieval problem; specifically, we demonstrate a sublinear-time compressive phase retrieval algorithm which is guaranteed to recover a given $s$-sparse vector ${\\bf x} \\in \\mathbb{C}^d$ with high probability in just $\\mathcal{O}(s \\log^5 s \\cdot \\log d)$-time using only $\\mathcal{O}(s \\log^4 s \\cdot \\log d)$ magnitude measurements. In doing so we demonstrate the existence of compressive phase retrieval algorithms with near-optimal linear-in-sparsity runtime complexities.","url_abs":"http://arxiv.org/abs/1501.02377v3","url_pdf":"http://arxiv.org/pdf/1501.02377v3.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":"fast-phase-retrieval-from-local-correlation","repo_url":"https://bitbucket.org/charms/blockpr","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}