Fast phase unwrapping via nonconvex regularization and tail-minimization

Fast phase unwrapping via nonconvex regularization and tail-minimization | 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 Fast phase unwrapping via nonconvex regularization and tail-minimization Kexin Li, Huibin Chang, Zhangling Chen, Zhifang Liu, Yutong Li, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7250729/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 8 You are reading this latest preprint version Abstract In the forefront of imaging technology, the limitations of modulo-$2\pi$ phase measurement significantly hinder the in-depth understanding and analysis of the underlying characteristics of images. As one of most typical phase unwrapping methods, variational regularization methods aremore interpretable and stable. This paper proposes a novel variational phase unwrapping model, that incorporates a non-convex anisotropic and isotropic total variation regularization and balances phase data compatibility constraints with box constraints to ensure the rationality and physical consistency of the solution space. It is solved using primal-dual hybrid gradient algorithm, which is theoretically proven to possess global convergence and demonstrates low computational cost in practice. To optimize algorithm performance and efficiency, we introduce tail-minimization mechanism, which precisely identifies and corrects cumulative errors in phase estimation during iterations while automatically excluding pixels that have already converged from subsequent computations, thereby significantly reducing computational load and accelerating the overall convergence process. Through a series of simulations, we comprehensively compared the proposed method with existing iterative phase unwrapping algorithms. Numerical results indicate that, particularly in handling highly complex and high-wrapping-phase data, the proposed algorithm exhibits superior recovery performance and stability. Especially, the signal-to-noise ratio (SNR) of the unwrapping results is dramatically improved, with our method achieving up to double the SNR values of competing methods. Phase unwrapping Nonconvex regularization Anisotropic and isotropic total variation regularization Primal-dual algorithm Tail-minimization Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 22 Apr, 2026 Reviews received at journal 20 Apr, 2026 Reviewers agreed at journal 21 Jan, 2026 Reviewers agreed at journal 24 Oct, 2025 Reviewers invited by journal 17 Sep, 2025 Editor assigned by journal 13 Sep, 2025 Submission checks completed at journal 31 Jul, 2025 First submitted to journal 30 Jul, 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7250729","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":516781035,"identity":"218f6be7-b215-4b9b-af95-413b71e92712","order_by":0,"name":"Kexin Li","email":"","orcid":"","institution":"Tianjin Normal University","correspondingAuthor":false,"prefix":"","firstName":"Kexin","middleName":"","lastName":"Li","suffix":""},{"id":516781039,"identity":"c27ff1e2-7899-4104-bfac-f4c91dc580d8","order_by":1,"name":"Huibin 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As one of most typical phase unwrapping methods, variational regularization methods aremore interpretable and stable. This paper proposes a novel variational phase unwrapping model, that incorporates a non-convex anisotropic and isotropic total variation regularization and balances phase data compatibility constraints with box constraints to ensure the rationality and physical consistency of the solution space. It is solved using primal-dual hybrid gradient algorithm, which is theoretically proven to possess global convergence and demonstrates low computational cost in practice. To optimize algorithm performance and efficiency, we introduce tail-minimization mechanism, which precisely identifies and corrects cumulative errors in phase estimation during iterations while automatically excluding pixels that have already converged from subsequent computations, thereby significantly reducing computational load and accelerating the overall convergence process. Through a series of simulations, we comprehensively compared the proposed method with existing iterative phase unwrapping algorithms. Numerical results indicate that, particularly in handling highly complex and high-wrapping-phase data, the proposed algorithm exhibits superior recovery performance and stability. 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