{"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/a-fast-and-provable-algorithm-for-sparse","title":"A Fast and Provable Algorithm for Sparse Phase Retrieval","arxiv_id":"2309.02046","date":"2023-09-05","proceeding":null,"authors":["Jian-Feng Cai","Yu Long","Ruixue Wen","Jiaxi Ying"],"abstract":"We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we propose an innovative second-order algorithm that employs a Newton-type method with hard thresholding. This algorithm overcomes the linear convergence limitations of first-order methods while preserving their hallmark per-iteration computational efficiency. We provide theoretical guarantees that our algorithm converges to the $s$-sparse ground truth signal $\\mathbf{x}^{\\natural} \\in \\mathbb{R}^n$ (up to a global sign) at a quadratic convergence rate after at most $O(\\log (\\Vert\\mathbf{x}^{\\natural} \\Vert /x_{\\min}^{\\natural}))$ iterations, using $\\Omega(s^2\\log n)$ Gaussian random samples. Numerical experiments show that our algorithm achieves a significantly faster convergence rate than state-of-the-art methods.","url_abs":"https://arxiv.org/abs/2309.02046v2","url_pdf":"https://arxiv.org/pdf/2309.02046v2.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":"a-fast-and-provable-algorithm-for-sparse","repo_url":"https://github.com/jxying/sparsepr","is_official":1,"mentioned_in_paper":1,"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}