Stochastic Alternating-Direction Expectation Propagation for High-Dimensional Inverse Problems in Imaging

Stochastic Alternating-Direction Expectation Propagation for High-Dimensional Inverse Problems in Imaging | 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 Stochastic Alternating-Direction Expectation Propagation for High-Dimensional Inverse Problems in Imaging Kehinde Olobatuyi, Oludare Ariyo, Robert Aykroyd This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7198218/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 It is a challenging task to reconstruct images from down-sampled and noisy measurements, such as Magnetic Resonance Imaging (MRI) and low-dose Computed Tomography (CT), due to the inherent mathematical ill-posedness of the inverse problem. This paper makes two contributions to Bayesian image reconstruction. Firstly, we propose stochastic alternating-direction expectation propagation (SAEP), a novel alternative to expectation propagation (EP), a family of variational inference algorithms. SAEP addresses the instability problem within EP due to negative variance. Secondly, we present SAEP as a black-box variational algorithm that leverages the Monte Carlo sampler to estimate the moments of the EP tilted distributions. SAEP allows scalable and robust Bayesian image reconstruction in cases where the tilted posterior is a mixture of different (unmatched) distributions that renders direct moment matching in Kullback-Leibler (KL) divergence infeasible. Further, as opposed to EP, which has no guarantee of convergence, SAEP can be shown to be convergent. We compared the performance of our SAEP algorithm to standard Markov Chain Monte Carlo (MCMC) on Gamma-camera imaging experiments and show that our SAEP algorithm outperforms MCMC in computing time while providing similar parameter estimates. Expectation Propagation Markov Chain Monte Carlo Alternating Direction Method of Multipliers Image Reconstruction Bayesian Models Gamma-camera Scans Computational Efficiency 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. 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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-7198218","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":492179900,"identity":"cc9697f9-7223-458a-abc4-6f58b38bd473","order_by":0,"name":"Kehinde Olobatuyi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7klEQVRIie3PMQrCMBSA4VcCcUnJqlTvUCm4KIo3MQh2dnFyEAqZqp2dvIJHUAJx0wO4VAQnZ6kgYtqqW1vdBPMPeUs+kgeg0/1iJcDJxCQZLQBURFBMem8y+IJASkTxvyhCMrxGgs2IkMch37HlBoUQjbNJxcNu3e8Jxk3uOnO+Z0uBbcOX2cQWpFEmMaGkYZmKzD2S/jaPVG4JoRdFtk9yzydW8orpY0VWLECKGDx/F6c6cB1OpLLbvhMgbK+ns2xCS548nFvN2sLvnywyatc4FYcwumSTV91JfBrPrVfFAKCTjtsnd3U6ne7fegCuFkjegVW8MwAAAABJRU5ErkJggg==","orcid":"","institution":"University of Victoria","correspondingAuthor":true,"prefix":"","firstName":"Kehinde","middleName":"","lastName":"Olobatuyi","suffix":""},{"id":492179901,"identity":"753dad82-861d-4226-8837-752d68f82ad4","order_by":1,"name":"Oludare Ariyo","email":"","orcid":"","institution":"University of Essex","correspondingAuthor":false,"prefix":"","firstName":"Oludare","middleName":"","lastName":"Ariyo","suffix":""},{"id":492179902,"identity":"5350d083-bded-4dfc-a9d3-e4f2005a3735","order_by":2,"name":"Robert Aykroyd","email":"","orcid":"","institution":"University of Leeds","correspondingAuthor":false,"prefix":"","firstName":"Robert","middleName":"","lastName":"Aykroyd","suffix":""}],"badges":[],"createdAt":"2025-07-23 15:53:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7198218/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7198218/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105300505,"identity":"e9550e1a-c3a1-4ad8-8e2b-d177baba888f","added_by":"auto","created_at":"2026-03-24 13:43:33","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1580716,"visible":true,"origin":"","legend":"","description":"","filename":"SSEPnew.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7198218/v1_covered_9d7bc0e2-0317-4678-a2d4-cbc068353888.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Stochastic Alternating-Direction Expectation Propagation for High-Dimensional Inverse Problems in Imaging","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":"Expectation Propagation, Markov Chain Monte Carlo, Alternating Direction Method of Multipliers, Image Reconstruction, Bayesian Models, Gamma-camera Scans, Computational Efficiency","lastPublishedDoi":"10.21203/rs.3.rs-7198218/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7198218/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"It is a challenging task to reconstruct images from down-sampled and noisy measurements, such as Magnetic Resonance Imaging (MRI) and low-dose Computed Tomography (CT), due to the inherent mathematical ill-posedness of the inverse problem. 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