{"paper_id":"2c209d9e-710c-48fd-aaaa-92c17bc48ef6","body_text":"Fourier perspectives on Gegenbauer polynomial smoothing | 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PDF Article Fourier perspectives on Gegenbauer polynomial smoothing Yue Wang, John Healy This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3837357/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 Gibbs ringing is an artifact that occurs physically in many signal and image acquisition modalities. Gegenbauer reconstruction is an approach to reducing Gibbs artifacts based on polynomial smoothing of continuous regions of the signal using Gegenbauer polynomials. In this work, we systematically explain Gegenbauer reconstruction in the signal processing context. We investigate how the parameters, lambda and m, impact the behavior of Gegenbauer reconstruction. We make a quantitative comparison between Gegenbauer reconstruction and other Gibbs suppression methods. Gegenbauer reconstruction assumes that the locations of the discontinuities are known, so we examined how faulty edge detection results could impact Gegenbauer reconstruction. Our results question the standing of Gegenbauer reconstruction in the literature as an exceptionally high performing method of Gibbs ringing reduction. Physical sciences/Engineering/Electrical and electronic engineering Physical sciences/Optics and photonics 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. 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