{"title":"一种三维有限Radon变换","authors":"Mustapha Boukour, A. E. Omri","doi":"10.17265/2159-5291/2019.02.005","DOIUrl":null,"url":null,"abstract":"The present work is devoted to the development of the extension of FRT (Finite Radon Transform) to the tridimensional case. One simple formulation is proposed and it is shown that it is the exact discretization of the continuous Discrete Radon Transform. More precisely this is the case when the sampling is given on a regular grid i.e. the continuous function is filtered by the mean of the box function. Relation of this transform with the Discrete Fourier one is given and is for some help in numerical implementation.","PeriodicalId":61124,"journal":{"name":"数学和系统科学:英文版","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A 3D Finite Radon Transform\",\"authors\":\"Mustapha Boukour, A. E. Omri\",\"doi\":\"10.17265/2159-5291/2019.02.005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The present work is devoted to the development of the extension of FRT (Finite Radon Transform) to the tridimensional case. One simple formulation is proposed and it is shown that it is the exact discretization of the continuous Discrete Radon Transform. More precisely this is the case when the sampling is given on a regular grid i.e. the continuous function is filtered by the mean of the box function. Relation of this transform with the Discrete Fourier one is given and is for some help in numerical implementation.\",\"PeriodicalId\":61124,\"journal\":{\"name\":\"数学和系统科学:英文版\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"数学和系统科学:英文版\",\"FirstCategoryId\":\"1089\",\"ListUrlMain\":\"https://doi.org/10.17265/2159-5291/2019.02.005\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"数学和系统科学:英文版","FirstCategoryId":"1089","ListUrlMain":"https://doi.org/10.17265/2159-5291/2019.02.005","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The present work is devoted to the development of the extension of FRT (Finite Radon Transform) to the tridimensional case. One simple formulation is proposed and it is shown that it is the exact discretization of the continuous Discrete Radon Transform. More precisely this is the case when the sampling is given on a regular grid i.e. the continuous function is filtered by the mean of the box function. Relation of this transform with the Discrete Fourier one is given and is for some help in numerical implementation.
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