计算（数值）直径方案中的计算机断层扫描问题与通过有限卷积恢复函数问题的等价性

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2024-02-28 DOI:10.3103/s1066369x23120095

N. Temirgaliyev, Sh. K. Abikenova, Sh. U. Azhgaliyev, Ye. Ye. Nurmoldin, G. E. Taugynbayeva, A. Zh. Zhubanysheva

{"title":"计算（数值）直径方案中的计算机断层扫描问题与通过有限卷积恢复函数问题的等价性","authors":"N. Temirgaliyev, Sh. K. Abikenova, Sh. U. Azhgaliyev, Ye. Ye. Nurmoldin, G. E. Taugynbayeva, A. Zh. Zhubanysheva","doi":"10.3103/s1066369x23120095","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The equivalence of the norms of deviations of the desired density of a body from operators such as finite density transformation with specially constructed elements and the Radon transformation from it is stated. It is shown how computer science, previously established in the theory of computational (numerical) diameter, immediately leads to nontrivial results in computed tomography.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"9 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Equivalence of Computed Tomography Problem with the Problem of Recovery of Functions by Finite Convolutions in a Scheme of Computational (Numerical) Diameter\",\"authors\":\"N. Temirgaliyev, Sh. K. Abikenova, Sh. U. Azhgaliyev, Ye. Ye. Nurmoldin, G. E. Taugynbayeva, A. Zh. Zhubanysheva\",\"doi\":\"10.3103/s1066369x23120095\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>The equivalence of the norms of deviations of the desired density of a body from operators such as finite density transformation with specially constructed elements and the Radon transformation from it is stated. It is shown how computer science, previously established in the theory of computational (numerical) diameter, immediately leads to nontrivial results in computed tomography.</p>\",\"PeriodicalId\":46110,\"journal\":{\"name\":\"Russian Mathematics\",\"volume\":\"9 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3103/s1066369x23120095\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066369x23120095","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要阐述了用专门构建的元素进行有限密度变换和 Radon 变换等算子求得的人体所需密度的偏差规范的等价性。它说明了以前在计算（数值）直径理论中建立的计算机科学如何立即导致计算断层扫描中的非难结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Equivalence of Computed Tomography Problem with the Problem of Recovery of Functions by Finite Convolutions in a Scheme of Computational (Numerical) Diameter

Abstract

The equivalence of the norms of deviations of the desired density of a body from operators such as finite density transformation with specially constructed elements and the Radon transformation from it is stated. It is shown how computer science, previously established in the theory of computational (numerical) diameter, immediately leads to nontrivial results in computed tomography.

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

来源期刊

Russian Mathematics MATHEMATICS-

CiteScore

0.90

自引率

25.00%

发文量

期刊介绍： Russian Mathematics is a peer reviewed periodical that encompasses the most significant research in both pure and applied mathematics.