Optimal sparse phase retrieval via a quasi-Bayesian approach

Optimal sparse phase retrieval via a quasi-Bayesian approach | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Optimal sparse phase retrieval via a quasi-Bayesian approach The Tien Mai This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6594833/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Nov, 2025 Read the published version in Statistics and Computing → Version 1 posted 9 You are reading this latest preprint version Abstract This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal needs to be reconstructed using only the magnitude of its transformation while phase information remains inaccessible. Leverag-ing the inherent sparsity of many real-world signals, we introduce a novel sparse quasi-Bayesian approach and provide the first theoretical guarantees for such an approach. Specifically, we employ a scaled Student’s t-distribution as a continuous shrinkage prior to enforce sparsity and analyze the method using the PAC-Bayesian inequality framework. Our results establish that the proposed Bayesian estimator achieves minimax-optimal convergence rates under sub-exponential noise, matching those of state-of-the-art frequentist methods. To ensure computational feasibility , we develop an efficient Langevin Monte Carlo sampling algorithm. Through numerical experiments, we demonstrate that our method performs comparably to existing frequentist techniques , highlighting its potential as a principled alternative for sparse phase retrieval in noisy settings. PAC-Bayes bounds sparsity minimax-optimal rate contraction rates Langevin Monte Carlo phase retrieval Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 21 Nov, 2025 Read the published version in Statistics and Computing → Version 1 posted Editorial decision: Revision requested 05 Sep, 2025 Reviews received at journal 05 Sep, 2025 Reviewers agreed at journal 05 Sep, 2025 Reviews received at journal 02 Sep, 2025 Reviewers agreed at journal 05 Jun, 2025 Reviewers invited by journal 23 May, 2025 Editor assigned by journal 06 May, 2025 Submission checks completed at journal 06 May, 2025 First submitted to journal 05 May, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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