Efficient quaternion CUR method for low-rank approximation to quaternion matrix

Efficient quaternion CUR method for low-rank approximation to quaternion matrix | 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 Efficient quaternion CUR method for low-rank approximation to quaternion matrix Pengling Wu, Kit Ian Kou, Hongmin Cai, Zhaoyuan Yu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3989824/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 22 Aug, 2024 Read the published version in Numerical Algorithms → Version 1 posted 4 You are reading this latest preprint version Abstract The low-rank quaternion matrix approximation has been successfully applied in many applications involving signal processing and color image processing. However, the cost of quaternion models for generating low-rank quaternion matrix approximation is sometimes considerable due to the computation of the quaternion singular value decomposition (QSVD), which limits their application to real large-scale data. To address this deficiency, an efficient quaternion matrix CUR (QMCUR) method for low-rank approximation is suggested , which provides significant acceleration in color image processing. We first explore the QMCUR approximation method, which uses actual columns and rows of the given quaternion matrix, instead of the costly QSVD. Additionally, two different sampling strategies are used to sample the above-selected columns and rows. Then, the perturbation analysis is performed on the QMCUR approximation of noisy versions of low-rank quater-nion matrices. Extensive experiments on both synthetic and real data further reveal the superiority of the proposed algorithm compared with other algorithms for getting low-rank approximation, in terms of both efficiency and accuracy. Quaternion matrix quaternion CUR decomposition low-rank approximation color image processing Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 22 Aug, 2024 Read the published version in Numerical Algorithms → Version 1 posted Editorial decision: Revision requested 04 Mar, 2024 Editor assigned by journal 04 Mar, 2024 Submission checks completed at journal 28 Feb, 2024 First submitted to journal 25 Feb, 2024 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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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-3989824","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":275366621,"identity":"70879bbb-b3b5-403e-9fc9-5bc177eb0177","order_by":0,"name":"Pengling Wu","email":"","orcid":"","institution":"University of Macau","correspondingAuthor":false,"prefix":"","firstName":"Pengling","middleName":"","lastName":"Wu","suffix":""},{"id":275366622,"identity":"c43ff7ad-0784-43ae-a7d2-842f2f641df8","order_by":1,"name":"Kit Ian Kou","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAp0lEQVRIiWNgGAWjYBACCWY2IFkBZhuQouUMSVoYgFoY20jRItnOlviYd97haAb25m0SjDk2hLVIM7MdNubddji3gedYmQTjtjTCWuSY2dukwVokcsyAWg4Tq2UOUIv8GyK1AB12TJq3AWQLD5FaJJvZkg3nHEvPbeNJK7ZIJMYvEuePGT54U2Od289+eOONj9uICDE4AMUoQwIJGkbBKBgFo2AU4AEAaC4vqlmhpNMAAAAASUVORK5CYII=","orcid":"","institution":"University of Macau","correspondingAuthor":true,"prefix":"","firstName":"Kit","middleName":"Ian","lastName":"Kou","suffix":""},{"id":275366623,"identity":"9faddeb5-b639-4cfc-a46a-d76347a8bd89","order_by":2,"name":"Hongmin Cai","email":"","orcid":"","institution":"South China University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Hongmin","middleName":"","lastName":"Cai","suffix":""},{"id":275366624,"identity":"d14f94b0-ec36-4c94-948b-5161a20ebdff","order_by":3,"name":"Zhaoyuan Yu","email":"","orcid":"","institution":"Nanjing Normal University","correspondingAuthor":false,"prefix":"","firstName":"Zhaoyuan","middleName":"","lastName":"Yu","suffix":""}],"badges":[],"createdAt":"2024-02-26 04:07:06","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3989824/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3989824/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11075-024-01923-8","type":"published","date":"2024-08-22T15:57:04+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":63300093,"identity":"d1fd9dc0-3e78-4702-a3c9-0ea99ca5c748","added_by":"auto","created_at":"2024-08-26 16:10:59","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6734857,"visible":true,"origin":"","legend":"","description":"","filename":"QMCUR.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3989824/v1_covered_a2c3e454-34a5-4b9c-871c-de81f064c516.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Efficient quaternion CUR method for low-rank approximation to quaternion matrix","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"numerical-algorithms","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"numa","sideBox":"Learn more about [Numerical Algorithms](http://link.springer.com/journal/11075)","snPcode":"11075","submissionUrl":"https://submission.nature.com/new-submission/11075/3","title":"Numerical Algorithms","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Quaternion matrix, quaternion CUR decomposition, low-rank approximation, color image processing","lastPublishedDoi":"10.21203/rs.3.rs-3989824/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3989824/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The low-rank quaternion matrix approximation has been successfully applied in many applications involving signal processing and color image processing. 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