Cebeiro Javier, Nguyen Mai K., Rollet Genevi`eve, Dumas Laurent
{"title":"AN ANALYTIC INVERSION FORMULA FOR A RADON TRANSFORM ON A CLASS OF CONES","authors":"Cebeiro Javier, Nguyen Mai K., Rollet Genevi`eve, Dumas Laurent","doi":"10.32523/2306-6172-2022-10-3-73-83","DOIUrl":null,"url":null,"abstract":"Since the works of Radon and Cormack on the classical Radon transform on straight lines, several generalizations involving integrations on conical surfaces have been studied. In this article, we introduce a new family of conical surfaces with arbitrary vertices of the space and axes through the origin and study the corresponding Radon transform. We derive its analytical inversion in two and three dimensions. Numerical simulations are carried out for the two-dimensional case.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32523/2306-6172-2022-10-3-73-83","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Since the works of Radon and Cormack on the classical Radon transform on straight lines, several generalizations involving integrations on conical surfaces have been studied. In this article, we introduce a new family of conical surfaces with arbitrary vertices of the space and axes through the origin and study the corresponding Radon transform. We derive its analytical inversion in two and three dimensions. Numerical simulations are carried out for the two-dimensional case.