Adaptive Parameter Selection Scheme for Hybrid Variation-based Image Denoising Model

Adaptive Parameter Selection Scheme for Hybrid Variation-based Image Denoising Model | 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 Adaptive Parameter Selection Scheme for Hybrid Variation-based Image Denoising Model Yuan Liu, Raymond Hon-fu Chan, Zhi-Feng Pang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7296041/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 11 You are reading this latest preprint version Abstract Regularization methods play a crucial role in addressing the ill-posedness of inverse problems in image denoising. The key to enhance denoising performance lies in the proper selection of regularization terms that effectively encode image priors and regularization parameters that align with the statistical characteristics of images. To tackle these challenges, this paper proposes a hybrid total variation denoising model, which integrates weighted total variation for edge preservation with higher-order total variation for smooth region preservation. The regularization parameter in the proposed model is adaptively determined using Morozov’s discrepancy principle, thereby improving the efficacy of denoising. Since the proposed model is convex and non-smooth, we employ the alternating direction method of multipliers (ADMM) to decompose the problem into computationally tractable subproblems. To enhance the robustness of ADMM, a strategy of norm error correction is introduced for primal variables and dual variables to refine the penalty parameters. Furthermore, since the proposed model and numerical algorithm eliminate the need for manual parameter tuning, they can be formulated as an unsupervised denoising framework based on algorithmic unfolding architecture. Extensive numerical experiments demonstrate that the proposed method not only outperforms several state-of-the-art techniques in overcoming the staircase effect and preserving local structural features but also exhibits competitive performance compared to representative deep learning-based denoising approaches. Adaptive regularization parameter selection Discrepancy principle Weighted total variation Alternating direction method of multipliers (ADMM) Image denoising. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 15 Dec, 2025 Reviews received at journal 13 Nov, 2025 Reviews received at journal 04 Nov, 2025 Reviewers agreed at journal 09 Oct, 2025 Reviewers agreed at journal 07 Oct, 2025 Reviewers agreed at journal 07 Oct, 2025 Reviewers agreed at journal 07 Oct, 2025 Reviewers invited by journal 18 Sep, 2025 Editor assigned by journal 13 Sep, 2025 Submission checks completed at journal 05 Aug, 2025 First submitted to journal 04 Aug, 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-7296041","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":521735584,"identity":"8f6d8f09-13b1-48eb-a736-879961d87bb8","order_by":0,"name":"Yuan Liu","email":"","orcid":"","institution":"Henan University","correspondingAuthor":false,"prefix":"","firstName":"Yuan","middleName":"","lastName":"Liu","suffix":""},{"id":521735585,"identity":"c1f7d505-5736-4947-bd17-f4ce29454e27","order_by":1,"name":"Raymond Hon-fu Chan","email":"","orcid":"","institution":"Lingnan 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The key to enhance denoising performance lies in the proper selection of regularization terms that effectively encode image priors and regularization parameters that align with the statistical characteristics of images. To tackle these challenges, this paper proposes a hybrid total variation denoising model, which integrates weighted total variation for edge preservation with higher-order total variation for smooth region preservation. The regularization parameter in the proposed model is adaptively determined using Morozov’s discrepancy principle, thereby improving the efficacy of denoising. Since the proposed model is convex and non-smooth, we employ the alternating direction method of multipliers (ADMM) to decompose the problem into computationally tractable subproblems. To enhance the robustness of ADMM, a strategy of norm error correction is introduced for primal variables and dual variables to refine the penalty parameters. Furthermore, since the proposed model and numerical algorithm eliminate the need for manual parameter tuning, they can be formulated as an unsupervised denoising framework based on algorithmic unfolding architecture. Extensive numerical experiments demonstrate that the proposed method not only outperforms several state-of-the-art techniques in overcoming the staircase effect and preserving local structural features but also exhibits competitive performance compared to representative deep learning-based denoising approaches.","manuscriptTitle":"Adaptive Parameter Selection Scheme for Hybrid Variation-based Image Denoising Model","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-29 16:05:40","doi":"10.21203/rs.3.rs-7296041/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-12-15T14:33:16+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-13T12:07:29+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-04T17:13:53+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"141528037820004108796215218661078664046","date":"2025-10-09T11:31:12+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"277208879513797771399500752378358691136","date":"2025-10-07T13:00:45+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"141528037820004108796215218661078664046","date":"2025-10-07T09:37:58+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"277208879513797771399500752378358691136","date":"2025-10-07T08:17:22+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-09-18T10:52:04+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-09-13T08:29:42+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-08-05T16:12:40+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Mathematical Imaging and Vision","date":"2025-08-05T03:57:51+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-mathematical-imaging-and-vision","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jmiv","sideBox":"Learn more about [Journal of Mathematical Imaging and Vision](http://link.springer.com/journal/10851)","snPcode":"10851","submissionUrl":"https://submission.nature.com/new-submission/10851/3","title":"Journal of Mathematical Imaging and Vision","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"d3f149c3-4b55-4adc-8acb-f4b4ac9908c5","owner":[],"postedDate":"September 29th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-12T02:53:12+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-29 16:05:40","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7296041","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7296041","identity":"rs-7296041","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}