Quaternion-based Deep Image Prior with Regularization by Denoising for Color Image Restoration

Quaternion-based Deep Image Prior with Regularization by Denoising for Color Image Restoration | 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 Quaternion-based Deep Image Prior with Regularization by Denoising for Color Image Restoration Qinghua Zhang, Liangtian He, Shaobing Gao, Liangjian Deng, Jun Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4699292/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Deep image prior (DIP) has demonstrated remarkable efficacy in addressing various imaging inverse problems by capitalizing on the inherent biases of deep convolutional architectures to implicitly regularize the solutions. However, its application to color images has been hampered by the conventional DIP method's treatment of color channels in isolation, ignoring their important inter-channel correlations. To mitigate this limitation, we extend the DIP framework from the real domain to the quaternion domain and propose a novel quaternion deep image prior (QDIP) model for color image restoration. More importantly, to enhance the recovery performance of QDIP and alleviate its susceptibility to the unfavorable overfitting issue, we propose incorporating the concept of regularization by denoising (RED). This approach leverages existing denoisers to regularize inverse problems and integrates the RED scheme into our QDIP model. Extensive experiments on color image denoising, deblurring, and super-resolution show that the proposed QDIP and QDIP-RED achieve highly competitive performance against many state-of-the-art alternatives in both quantitative and qualitative evaluations. The dataset and code can be available at: https://github.com/qiuxuanzhizi/QDIP-RED Color image restoration Quaternion representation Deep image prior Regularization by denoising Quaternion ADMM Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-4699292","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":332740847,"identity":"cafb8a7e-56ca-4b3a-8aad-177b8848b046","order_by":0,"name":"Qinghua Zhang","email":"","orcid":"","institution":"Anhui University","correspondingAuthor":false,"prefix":"","firstName":"Qinghua","middleName":"","lastName":"Zhang","suffix":""},{"id":332740848,"identity":"19c55f03-45ad-48c6-ba5e-78aa6c23d433","order_by":1,"name":"Liangtian He","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAArklEQVRIiWNgGAWjYBACAwbmBoYPDAcgbCK1MDY2ziBZSzMPSVrM2RvbH9vU3ElsYG/eJsFQc4ewFsueg43NOceeJTbwHCuTYDj2jAiH3UgEamE7nNggkWMmwdhwmAgt9x82Nlv8A2qRf0OslhtA7zO2gWzhIVbLmcTGmb19h43beNKKLRKOEaPl+OEDH358Oyzbz354440PNURogQM2EJFAgoZRMApGwSgYBXgAAJF9QBKVNSDeAAAAAElFTkSuQmCC","orcid":"","institution":"Anhui University","correspondingAuthor":true,"prefix":"","firstName":"Liangtian","middleName":"","lastName":"He","suffix":""},{"id":332740849,"identity":"0af9f5fc-9bbe-4b2e-8286-30c6acfc1f91","order_by":2,"name":"Shaobing Gao","email":"","orcid":"","institution":"Sichuan University","correspondingAuthor":false,"prefix":"","firstName":"Shaobing","middleName":"","lastName":"Gao","suffix":""},{"id":332740850,"identity":"3cf03f9d-5938-45c7-b08e-046fd31615a9","order_by":3,"name":"Liangjian Deng","email":"","orcid":"","institution":"University of Electronic Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Liangjian","middleName":"","lastName":"Deng","suffix":""},{"id":332740851,"identity":"4a7a2376-a612-4121-94c7-72ae3d2b26bf","order_by":4,"name":"Jun Liu","email":"","orcid":"","institution":"Northeast Normal University","correspondingAuthor":false,"prefix":"","firstName":"Jun","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2024-07-07 08:08:47","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4699292/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4699292/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":63402004,"identity":"a37bcfaa-84e8-42bd-a15f-4cbb4239f911","added_by":"auto","created_at":"2024-08-27 19:05:09","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1887241,"visible":true,"origin":"","legend":"","description":"","filename":"QDIPREDTVCJ.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4699292/v1_covered_f67d8a1b-c211-48e3-9f18-9a11561b0c4e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Quaternion-based Deep Image Prior with Regularization by Denoising for Color Image Restoration","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Color image restoration, Quaternion representation, Deep image prior, Regularization by denoising, Quaternion ADMM","lastPublishedDoi":"10.21203/rs.3.rs-4699292/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4699292/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDeep image prior (DIP) has demonstrated remarkable efficacy in addressing various imaging inverse problems by capitalizing on the inherent biases of deep convolutional architectures to implicitly regularize the solutions. However, its application to color images has been hampered by the conventional DIP method's treatment of color channels in isolation, ignoring their important inter-channel correlations. To mitigate this limitation, we extend the DIP framework from the real domain to the quaternion domain and propose a novel quaternion deep image prior (QDIP) model for color image restoration. More importantly, to enhance the recovery performance of QDIP and alleviate its susceptibility to the unfavorable overfitting issue, we propose incorporating the concept of regularization by denoising (RED). This approach leverages existing denoisers to regularize inverse problems and integrates the RED scheme into our QDIP model. Extensive experiments on color image denoising, deblurring, and super-resolution show that the proposed QDIP and QDIP-RED achieve highly competitive performance against many state-of-the-art alternatives in both quantitative and qualitative evaluations. 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