一类锥体上radon变换的解析反演公式

Pub Date : 2022-09-27 DOI:10.32523/2306-6172-2022-10-3-73-83

Cebeiro Javier, Nguyen Mai K., Rollet Genevi`eve, Dumas Laurent

{"title":"一类锥体上radon变换的解析反演公式","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":"{\"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}","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

摘要

自Radon和Cormack关于直线上经典Radon变换的工作以来，研究了几种涉及圆锥曲面上积分的推广。本文通过原点引入了一种新的具有空间任意顶点和轴的圆锥曲面族，并研究了相应的Radon变换。我们推导了它在二维和三维的解析反演。对二维情况进行了数值模拟。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

AN ANALYTIC INVERSION FORMULA FOR A RADON TRANSFORM ON A CLASS OF CONES

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助