{"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/perturbed-amplitude-flow-for-phase-retrieval","title":"Perturbed Amplitude Flow for Phase Retrieval","arxiv_id":"1904.10307","date":"2019-04-23","proceeding":null,"authors":["Bing Gao","Xinwei Sun","Yang Wang","Zhiqiang Xu"],"abstract":"In this paper, we propose a new non-convex algorithm for solving the phase retrieval problem, i.e., the reconstruction of a signal $ \\vx\\in\\H^n $ ($\\H=\\R$ or $\\C$) from phaseless samples $ b_j=\\abs{\\langle \\va_j, \\vx\\rangle } $, $ j=1,\\ldots,m $. The proposed algorithm solves a new proposed model, perturbed amplitude-based model, for phase retrieval and is correspondingly named as {\\em Perturbed Amplitude Flow} (PAF). We prove that PAF can recover $c\\vx$ ($\\abs{c} = 1$) under $\\mathcal{O}(n)$ Gaussian random measurements (optimal order of measurements). Starting with a designed initial point, our PAF algorithm iteratively converges to the true solution at a linear rate for both real and complex signals. Besides, PAF algorithm needn't any truncation or re-weighted procedure, so it enjoys simplicity for implementation. The effectiveness and benefit of the proposed method are validated by both the simulation studies and the experiment of recovering natural images.","url_abs":"http://arxiv.org/abs/1904.10307v2","url_pdf":"http://arxiv.org/pdf/1904.10307v2.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":"perturbed-amplitude-flow-for-phase-retrieval","repo_url":"https://github.com/Ford666/Perturbed-amplitude-flow","is_official":0,"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}