Real-Time Compressive Sensing Framework Using 2D Hadamard Total Sequency Ordering

Real-Time Compressive Sensing Framework Using 2D Hadamard Total Sequency Ordering | 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 Real-Time Compressive Sensing Framework Using 2D Hadamard Total Sequency Ordering Mohammad Amiri, Alireza Ghafari This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8202915/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 Compressive sensing (CS) has emerged as a powerful framework for reducing the number of measurements required for accurate image reconstruction, making it especially relevant in applications such as medical imaging, wireless sensing, and single-pixel imaging. In CS, deterministic transforms like the Hadamard basis offer advantages in efficiency and hardware implementation. However, achieving high-quality reconstruction at low sampling ratios remains challenging, particularly because traditional random or fixed-order sampling patterns introduce redundancy and limit reconstruction performance. Existing Hadamard reordering methods, such as Walsh, cake-cutting, and weight ordering, partially address these issues but still struggle to balance reconstruction quality with computational efficiency in real-time or resource-limited environments. Deep learning-based CS approaches improve reconstruction accuracy but require large training datasets, high computational cost, and powerful hardware. To address these limitations, this study introduces a Total Sequency (TS)–based reordering of the Hadamard matrix, which prioritizes two-dimensional low-frequency patterns by counting sign changes across both rows and columns. This approach enhances sampling efficiency at very low sampling ratios while maintaining extremely low computational overhead. Integrated into a block-based CS pipeline, the proposed method delivers improved reconstruction accuracy at low sampling ratios, achieving average PSNR values of 19.61 dB, 22.21 dB, and 24.38 dB at sampling ratios of 0.01, 0.04, and 0.1, outperforming Walsh, cake-cutting, and weight ordering methods. Furthermore, it provides near-real-time reconstruction with processing times as low as 0.0014 seconds on a standard CPU, significantly faster than deep learning models such as CPP-Net. These findings demonstrate that TS-based Hadamard reordering bridges the gap between deterministic CS sampling and computational efficiency, making it highly suitable for portable imaging devices, wireless sensor networks, and other real-time, resource-constrained platforms. Theoretical Computer Science Artificial Intelligence and Machine Learning Compressive Sensing Hadamard Matrix Image Reconstruction Total Sequency Full Text Additional Declarations The authors declare no competing interests. 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-8202915","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":550553824,"identity":"7b5c880a-c5f4-4ba0-864c-a90faa8425f2","order_by":0,"name":"Mohammad Amiri","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsUlEQVRIiWNgGAWjYLCCBAYJORibh2gtxjClRGoBgsQeopXqNjA/3fBwj0X6fokcA4YfNQwy5g0EtJgdYDO7kfBMIrcHqIWx5xgDj8wBQlruPwBqOQDUwnPGgIG3gYFHgpDDzA6wfwNpSecBamH8S5wWHrAtCTzsPQbMRNrCUwbSYthzvK3gsMwxCaIctu3mjwN18uzNzBsfvqmxsSeoBQUcYGAgTcMoGAWjYBSMAhwAAKCxNsxb5RWMAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-9692-8721","institution":"Technical and Vocational University, Tehran, Iran","correspondingAuthor":true,"prefix":"","firstName":"Mohammad","middleName":"","lastName":"Amiri","suffix":""},{"id":550553948,"identity":"efec405d-82c3-49bb-91df-861665315f20","order_by":1,"name":"Alireza Ghafari","email":"","orcid":"","institution":"Amirkabir University","correspondingAuthor":false,"prefix":"","firstName":"Alireza","middleName":"","lastName":"Ghafari","suffix":""}],"badges":[],"createdAt":"2025-11-25 11:54:10","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8202915/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8202915/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":96917165,"identity":"420b44a8-0450-4a5e-954f-3d44dec35397","added_by":"auto","created_at":"2025-11-27 14:09:19","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":727073,"visible":true,"origin":"","legend":"","description":"","filename":"paperghafaricsv2revised1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8202915/v1_covered_57b9ac21-b57c-4e57-b526-c1486a436d06.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eReal-Time Compressive Sensing Framework Using 2D Hadamard Total Sequency Ordering\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Technical and vocational university, Tehran, Iran","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":"Compressive Sensing, Hadamard Matrix, Image Reconstruction, Total Sequency","lastPublishedDoi":"10.21203/rs.3.rs-8202915/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8202915/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCompressive sensing (CS) has emerged as a powerful framework for reducing the number of measurements required for accurate image reconstruction, making it especially relevant in applications such as medical imaging, wireless sensing, and single-pixel imaging. 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