Correlation Regularized Image Denoising via Low Rank Matrix Approximation

Correlation Regularized Image Denoising via Low Rank Matrix Approximation | 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 Correlation Regularized Image Denoising via Low Rank Matrix Approximation hüseyin özkaramanlı This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6015983/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 In this paper, we propose a new residual correlation based regularization method for image denoising and formulate the problem in the framework of Low Rank Matrix Approximation. For this purpose we propose an objective function which leads naturally to the weighted nuclear norm minimization. The objective function consists of a fidelity term and a regularization term which are the Frobenious norms of residual noise and the deviation of residual noise correlations from the true correlations. Convexity of the objective function is established and the closed form global minimum is obtained. A simple closed form formula for the residual noise singular values is derived. The formula involves the right singular vectors of the noisy observation matrix and the noise correlation matrix. Our solution explicitly shows how each singular value of the noisy observation matrix is thresholded to obtain the clean signal singular values. Hard and soft thresholding as well as the weighted thresholding of singular values come out as solutions of the proposed optimization problem. Simulation results in image denoising show that the proposed method performs as good as the weighted nuclear norm minimization method with better performance for most standard test images especially at high noise levels. Image denoising singular value thresholding nuclear norm minimization low-rank approximation correlation regularization 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-6015983","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":416355371,"identity":"b6660e38-193c-46fe-9d53-0e44466a48ec","order_by":0,"name":"hüseyin özkaramanlı","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABL0lEQVRIiWNgGAWjYBACAwTJBhViZ2x8AGElEKuFmbHZAK7lAC4tDChaGNgk8Gkxl0h/+Jin4A4DP/+xxM8VNdvkzZmZ2yo+5hxm4GfPMWD+uAdDi+WMHGNjHoNnDJINxw5Lnjl223BnM2PbzZnbDjNI9rwxYDjwDNNhN3LYpHkMDjMYHGxvkGxgu8244TBj221eoBagFFALpssMbqQ//w3Wcpi9+WfDv9v2IC3Ff4Fa7HFqSTBjBms5xnZMsrHtdiJICzMjyBYJHFrOvDGWnGNwmEeyhy3NsrHvdjJQS7Nk77Z0HokzzwoOnMGi5Xj6ww9v/hyWA4aY8c2Gb7dtNxxvf/jh5zZrOf725I0PKrCEMhAw8TAw8GCIgkWwa2BgYPyBQ2IUjIJRMApGARgAAJZUdFpOFde8AAAAAElFTkSuQmCC","orcid":"","institution":"Eastern Mediterranean University","correspondingAuthor":true,"prefix":"","firstName":"hüseyin","middleName":"","lastName":"özkaramanlı","suffix":""}],"badges":[],"createdAt":"2025-02-12 14:23:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6015983/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6015983/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":89615719,"identity":"ec75f8ae-d495-4cbd-a5e7-4059cee0b7ae","added_by":"auto","created_at":"2025-08-22 02:46:51","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":501028,"visible":true,"origin":"","legend":"","description":"","filename":"SignalImageandVideoProcessingCorrelationRegularizedImageDenoisingviaLRMAfeb25.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6015983/v1_covered_f4eae31a-6a1b-4ebf-925f-6c7ad1aa0eac.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Correlation Regularized Image Denoising via Low Rank Matrix Approximation","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":"Image denoising, singular value thresholding, nuclear norm minimization, low-rank approximation, correlation regularization","lastPublishedDoi":"10.21203/rs.3.rs-6015983/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6015983/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, we propose a new residual correlation based regularization method for image denoising and formulate the problem in the framework of Low Rank Matrix Approximation. For this purpose we propose an objective function which leads naturally to the weighted nuclear norm minimization. The objective function consists of a fidelity term and a regularization term which are the Frobenious norms of residual noise and the deviation of residual noise correlations from the true correlations. Convexity of the objective function is established and the closed form global minimum is obtained. A simple closed form formula for the residual noise singular values is derived. The formula involves the right singular vectors of the noisy observation matrix and the noise correlation matrix. Our solution explicitly shows how each singular value of the noisy observation matrix is thresholded to obtain the clean signal singular values. Hard and soft thresholding as well as the weighted thresholding of singular values come out as solutions of the proposed optimization problem. Simulation results in image denoising show that the proposed method performs as good as the weighted nuclear norm minimization method with better performance for most standard test images especially at high noise levels.\u003c/p\u003e","manuscriptTitle":"Correlation Regularized Image Denoising via Low Rank Matrix Approximation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-02-17 06:42:27","doi":"10.21203/rs.3.rs-6015983/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"1354b943-dc13-42c7-bf08-ed4ef4642921","owner":[],"postedDate":"February 17th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-08-22T02:38:42+00:00","versionOfRecord":[],"versionCreatedAt":"2025-02-17 06:42:27","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6015983","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6015983","identity":"rs-6015983","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}