{"title":"Analysis of View Aliasing for the Generalized Radon Transform in [math]","authors":"Alexander Katsevich","doi":"10.1137/23m1554746","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 415-440, March 2024. <br/> Abstract. In this paper we consider the generalized Radon transform [math] in the plane. Let [math] be a piecewise smooth function, which has a jump across a smooth curve [math]. We obtain a formula, which accurately describes view aliasing artifacts away from [math] when [math] is reconstructed from the data [math] discretized in the view direction. The formula is asymptotic, it is established in the limit as the sampling rate [math]. The proposed approach does not require that [math] be band-limited. Numerical experiments with the classical Radon transform and generalized Radon transform (which integrates over circles) demonstrate the accuracy of the formula.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1554746","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
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Abstract
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 415-440, March 2024. Abstract. In this paper we consider the generalized Radon transform [math] in the plane. Let [math] be a piecewise smooth function, which has a jump across a smooth curve [math]. We obtain a formula, which accurately describes view aliasing artifacts away from [math] when [math] is reconstructed from the data [math] discretized in the view direction. The formula is asymptotic, it is established in the limit as the sampling rate [math]. The proposed approach does not require that [math] be band-limited. Numerical experiments with the classical Radon transform and generalized Radon transform (which integrates over circles) demonstrate the accuracy of the formula.
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